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0001 Automatically generated by Mendeley 1.3.1
0002 Any changes to this file will be lost if it is regenerated by Mendeley.
0003 
0004 @article{BBM10,
0005 author = {Barret, Florent and Bovier, Anton and M\'{e}l\'{e}ard, Sylvie},
0006 file = {::},
0007 journal = {Electronic Journal of Probability},
0008 pages = {323--345},
0009 publisher = {Institute of Mathematical Statistics},
0010 title = {{Uniform estimates for metastable transition times in a coupled bistable system}},
0011 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/viewarticle52a2.html?id=2066&layout=abstract},
0012 volume = {15},
0013 year = {2010}
0014 }
0015 @book{Dembo2009,
0016 author = {Dembo, A. and Zeitouni, O.},
0017 booktitle = {Media},
0018 file = {::},
0019 isbn = {9783642033100},
0020 publisher = {Springer Verlag},
0021 title = {{Large deviations techniques and applications}},
0022 url = {http://books.google.com/books?hl=en&lr=&id=iT9JRlGPx5gC&oi=fnd&pg=PR7&dq=Large+deviations+techniques+and+applications&ots=dXUizjv55r&sig=lNsDVpsNmNhQLtXa4A0svmed95I},
0023 volume = {38},
0024 year = {2009}
0025 }
0026 @article{gyongy.millet05,
0027 author = {Gy\"{o}ngy, Istv\'{a}n and Millet, Annie},
0028 file = {::},
0029 journal = {Potential Analysis},
0030 keywords = {coercivity,finite elements,monotone operators,stochastic evolution equations},
0031 number = {2},
0032 pages = {99--134},
0033 publisher = {Springer},
0034 title = {{On discretization schemes for stochastic evolution equations}},
0035 url = {http://www.springerlink.com/index/P8R487477340T18R.pdf},
0036 volume = {23},
0037 year = {2005}
0038 }
0039 @book{gilbarg.trudinger01,
0040 author = {Gilbarg, David and Trudinger, Neil S.},
0041 pages = {xiv+517},
0042 publisher = {Springer-Verlag},
0043 title = {{Elliptic partial differential equations of second order}},
0044 url = {http://books.google.com/books?hl=en&lr=&id=eoiGTf4cmhwC&oi=fnd&pg=PA1&dq=Elliptic+partial+differential+equations+of+second+order&ots=kOOFk0gSrH&sig=N_OKR1m9GUvkobnWhM93uB-e34E},
0045 year = {2001}
0046 }
0047 @article{Winder2007,
0048 author = {Winder, Nick},
0049 file = {::},
0050 journal = {Ecology and Society},
0051 keywords = {adaptive potential,complex adaptive systems,cultural ecodynamics,innovation,metastability,resilience},
0052 number = {2},
0053 title = {{Innovation and metastability: A systems model}},
0054 url = {http://www.ibcperu.org/doc/isis/8159.pdf},
0055 volume = {12},
0056 year = {2007}
0057 }
0058 @article{daprato.debussche03,
0059 author = {{Da Prato}, Giuseppe and Debussche, Arnaud},
0060 file = {::},
0061 journal = {The Annals of Probability},
0062 number = {4},
0063 pages = {1900--1916},
0064 publisher = {Institute of Mathematical Statistics},
0065 title = {{Strong solutions to the stochastic quantization equations}},
0066 url = {http://projecteuclid.org/euclid.aop/1068646370},
0067 volume = {31},
0068 year = {2003}
0069 }
0070 @article{Anderssen1984,
0071 author = {Anderssen, RS},
0072 file = {::},
0073 journal = {BIT Numerical Mathematics},
0074 number = {January},
0075 pages = {401--412},
0076 title = {{On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions}},
0077 url = {http://www.springerlink.com/index/Q75534227QJ860V6.pdf},
0078 volume = {24},
0079 year = {1984}
0080 }
0081 @article{Berard1999,
0082 author = {Berard, A. and Grandati, Y.},
0083 file = {::},
0084 journal = {International journal of theoretical physics},
0085 number = {10},
0086 pages = {2535--2548},
0087 publisher = {Springer},
0088 title = {{Stochastic Quantization Approach for the Ising Model}},
0089 url = {http://www.springerlink.com/index/U184362764X571H6.pdf},
0090 volume = {38},
0091 year = {1999}
0092 }
0093 @article{Jiang1994,
0094 author = {Jiang, J.F.},
0095 file = {::},
0096 journal = {Journal of mathematical analysis and applications},
0097 number = {1},
0098 pages = {92--100},
0099 publisher = {Elsevier},
0100 title = {{Three-and four-dimensional cooperative systems with every equilibrium stable}},
0101 url = {http://www.sciencedirect.com/science/article/pii/S0022247X84714132},
0102 volume = {188},
0103 year = {1994}
0104 }
0105 @article{Funaki2004,
0106 author = {Funaki, Tadahisa},
0107 doi = {10.1214/009117904000000199},
0108 file = {::},
0109 issn = {0091-1798},
0110 journal = {The Annals of Probability},
0111 month = apr,
0112 number = {2},
0113 pages = {1201--1227},
0114 title = {{Zero temperature limit for interacting Brownian particles. I. Motion of a single body}},
0115 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884850/ http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884849/},
0116 volume = {32},
0117 year = {2004}
0118 }
0119 @incollection{bovier03,
0120 author = {Bovier, Anton},
0121 booktitle = {Lecture Notes TUB},
0122 file = {::},
0123 pages = {1--75},
0124 title = {{Markov processes and metastability}},
0125 url = {http://www-wt.iam.uni-bonn.de/$\sim$bovier/files/metavor.pdf},
0126 year = {2003}
0127 }
0128 @article{Mikami1990,
0129 author = {Mikami, T.},
0130 file = {::},
0131 journal = {The Annals of Probability},
0132 number = {2},
0133 pages = {524--536},
0134 publisher = {Institute of Mathematical Statistics},
0135 title = {{Asymptotic analysis of invariant density of randomly perturbed dynamical systems}},
0136 url = {http://projecteuclid.org/euclid.aop/1176990843},
0137 volume = {18},
0138 year = {1990}
0139 }
0140 @article{Mezard2001,
0141 archivePrefix = {arXiv},
0142 arxivId = {arXiv:cond-mat/0009418v1},
0143 author = {M\'{e}zard, Marc and Parisi, Giorgio},
0144 eprint = {0009418v1},
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0146 journal = {The European Physical Journal B-Condensed Matter and Complex Systems},
0147 number = {2},
0148 pages = {217--233},
0149 primaryClass = {arXiv:cond-mat},
0150 publisher = {Springer},
0151 title = {{The Bethe lattice spin glass revisited}},
0152 url = {http://www.springerlink.com/index/mg5p2ay9m48hlcw2.pdf},
0153 volume = {20},
0154 year = {2001}
0155 }
0156 @article{Dembo2005,
0157 author = {Dembo, A.},
0158 file = {::},
0159 journal = {Lectures on Probability Theory and Statistics},
0160 pages = {1--101},
0161 publisher = {Springer},
0162 title = {{Favorite points, cover times and fractals}},
0163 url = {http://www.springerlink.com/index/y7r377244560k334.pdf},
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0165 year = {2005}
0166 }
0167 @article{VdEW08,
0168 author = {Vanden-Eijnden, Eric and Westdickenberg, Maria G.},
0169 doi = {10.1007/s10955-008-9537-8},
0170 file = {::},
0171 isbn = {1095500895378},
0172 issn = {0022-4715},
0173 journal = {Journal of Statistical Physics},
0174 keywords = {large deviation theory,metastability,nucleation,phase transformation,rare events,small noise,spatially extended system,stochastic partial differential equation},
0175 month = apr,
0176 number = {6},
0177 pages = {1023--1038},
0178 title = {{{Rare Events in Sto\-chas\-tic Partial Differential Equations on Large Spatial Domains}}},
0179 url = {http://www.springerlink.com/index/10.1007/s10955-008-9537-8},
0180 volume = {131},
0181 year = {2008}
0182 }
0183 @article{Chapuy2009,
0184 author = {Chapuy, Guillaume},
0185 doi = {10.1017/S0000000000000000},
0186 file = {::},
0187 isbn = {0000000000000},
0188 journal = {Combinatorics, Probability and Computing},
0189 keywords = {algebraic series,asymptotic combinatorics,bijec-,graphs on surfaces},
0190 number = {04},
0191 pages = {477--516},
0192 publisher = {Cambridge Univ Press},
0193 title = {{Asymptotic enumeration of constellations and related families of maps on orientable surfaces}},
0194 url = {http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=5794560},
0195 volume = {18},
0196 year = {2009}
0197 }
0198 @article{Bak2002,
0199 author = {Bak, JG and Shkalikov, A. A.},
0200 file = {::},
0201 journal = {Mathematical Notes},
0202 keywords = {distribution potentials,multipliers,schr,sobolev spaces},
0203 number = {5},
0204 pages = {587--594},
0205 publisher = {Springer},
0206 title = {{Multipliers in Dual Sobolev Spaces and Schr\"{o}dinger Operators with Distribution Potentials}},
0207 url = {http://www.springerlink.com/index/E7J8GP8W5EVNGQ2H.pdf},
0208 volume = {71},
0209 year = {2002}
0210 }
0211 @article{Kalton2007,
0212 author = {Kalton, NJ and Mayboroda, Svitlana and Mitrea, Marius},
0213 file = {::},
0214 journal = {Contemporary Mathematics},
0215 pages = {121},
0216 publisher = {Providence, RI; American Mathematical Society; 1999},
0217 title = {{Interpolation of Hardy-Sobolev-Besov-Triebel-Lizorkin spaces and applications to problems in partial differential equations}},
0218 url = {http://www.math.purdue.edu/$\sim$svitlana/milman_conf.pdf},
0219 volume = {445},
0220 year = {2007}
0221 }
0222 @misc{Malrieu2006,
0223 author = {Malrieu, F.},
0224 booktitle = {perso.univ-rennes1.fr},
0225 file = {::},
0226 title = {{Processus de Markov et in\'{e}galit\'{e}s fonctionnelles}},
0227 url = {http://perso.univ-rennes1.fr/florent.malrieu/MASTER2/markov180406.pdf},
0228 year = {2006}
0229 }
0230 @article{Mugnai2007a,
0231 archivePrefix = {arXiv},
0232 arxivId = {arXiv:0704.1954v2},
0233 author = {Mugnai, Luca and R\"{o}ger, Matthias},
0234 eprint = {arXiv:0704.1954v2},
0235 file = {::},
0236 journal = {Arxiv preprint arXiv:0704.1954},
0237 pages = {1--33},
0238 title = {{The Allen-Cahn action functional in higher dimensions}},
0239 url = {http://arxiv.org/abs/0704.1954},
0240 volume = {1},
0241 year = {2007}
0242 }
0243 @article{Herrmann2008,
0244 author = {Herrmann, Samuel and Imkeller, Peter and Peithmann, Dierk},
0245 doi = {10.1214/07-AAP489},
0246 file = {::},
0247 issn = {1050-5164},
0248 journal = {The Annals of Applied Probability},
0249 month = aug,
0250 number = {4},
0251 pages = {1379--1423},
0252 title = {{Large deviations and a Kramers’ type law for self-stabilizing diffusions}},
0253 url = {http://projecteuclid.org/euclid.aoap/1216677126},
0254 volume = {18},
0255 year = {2008}
0256 }
0257 @article{Morosi2010,
0258 archivePrefix = {arXiv},
0259 arxivId = {arXiv:0902.0708v1},
0260 author = {Morosi, Carlo and Pizzocchero, Livio},
0261 eprint = {arXiv:0902.0708v1},
0262 file = {::},
0263 journal = {Advances in Applied Mathematics},
0264 keywords = {26d10,46e35,47a60,ams 2000 subject classifications,inequalities,pointwise multiplication,sobolev spaces},
0265 number = {4},
0266 pages = {393--432},
0267 publisher = {Elsevier},
0268 title = {{New results on multiplication in Sobolev spaces}},
0269 url = {http://www.sciencedirect.com/science/article/pii/S0196885809001250},
0270 volume = {44},
0271 year = {2010}
0272 }
0273 @inproceedings{Voros1993,
0274 author = {Voros, A.},
0275 booktitle = {Annales de l'institut Fourier},
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0277 number = {5},
0278 pages = {1509--1534},
0279 publisher = {Chartres: L'Institut, 1950-},
0280 title = {{R\'{e}surgence quantique}},
0281 url = {http://archive.numdam.org/article/AIF_1993__43_5_1509_0.pdf},
0282 volume = {43},
0283 year = {1993}
0284 }
0285 @article{Yoo2000,
0286 author = {Yoo, Hyek},
0287 file = {::},
0288 journal = {Mathematics of Computation},
0289 keywords = {and phrases,c 2000 american mathematical,embedding theorems,finite-difference method,potentials,rate of convergence,society,stochastic partial differential equations,weighted spaces of bessel},
0290 number = {230},
0291 pages = {653--666},
0292 title = {{Semi-discretization of stochastic partial differential equations on R1 by a finite-difference method}},
0293 url = {http://www.ams.org/mcom/2000-69-230/S0025-5718-99-01150-3/S0025-5718-99-01150-3.pdf},
0294 volume = {69},
0295 year = {2000}
0296 }
0297 @article{Sandier2004,
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0300 journal = {Communications on pure and applied mathematics},
0301 number = {12},
0302 pages = {1627--1672},
0303 publisher = {Wiley Online Library},
0304 title = {{Gamma-convergence of gradient flows with applications to Ginzburg-Landau}},
0305 url = {http://onlinelibrary.wiley.com/doi/10.1002/cpa.20046/abstract},
0306 volume = {57},
0307 year = {2004}
0308 }
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0311 doi = {10.1007/s00440-008-0150-1},
0312 file = {::;::},
0313 issn = {0178-8051},
0314 journal = {Probability Theory and Related Fields},
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0316 month = apr,
0317 number = {3-4},
0318 pages = {371--427},
0319 title = {{Hitting probabilities for systems of non-linear stochastic heat equations with multiplicative noise}},
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0330 publisher = {Providence, RI [etc.] American Mathematical Society.},
0331 title = {{On the determinant of elliptic boundary value problems on a line segment}},
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0340 number = {3},
0341 pages = {1135--1159},
0342 publisher = {JSTOR},
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0374 volume = {60},
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0378 author = {Allen, L},
0379 doi = {10.1016/S0040-5809(03)00104-7},
0380 file = {::},
0381 issn = {00405809},
0382 journal = {Theoretical Population Biology},
0383 keywords = {birth and death process,logistic equation,markov chain,persistence time,stochastic differential equation},
0384 month = dec,
0385 number = {4},
0386 pages = {439--449},
0387 title = {{A comparison of three different stochastic population models with regard to persistence time}},
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0392 @article{Hairer2007b,
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0395 file = {::},
0396 issn = {1050-5164},
0397 journal = {The Annals of Applied Probability},
0398 month = oct,
0399 number = {5/6},
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0401 title = {{Analysis of SPDEs arising in path sampling part II: The nonlinear case}},
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0403 volume = {17},
0404 year = {2007}
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0406 @article{BEGK00,
0407 archivePrefix = {arXiv},
0408 arxivId = {arXiv:cond-mat/0007343v1},
0409 author = {Bovier, Anton and Eckhoff, Michael and Gayrard, V\'{e}ronique and Klein, Markus},
0410 eprint = {0007343v1},
0411 file = {::},
0412 journal = {Journal of Physics A: Mathematical and General},
0413 keywords = {eigenvalue problems,exponential distribution,markov chains,metastability},
0414 pages = {L447},
0415 primaryClass = {arXiv:cond-mat},
0416 publisher = {IOP Publishing},
0417 title = {{Metastability and small eigenvalues in Markov chains}},
0418 url = {http://iopscience.iop.org/0305-4470/33/46/102},
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0420 year = {2000}
0421 }
0422 @book{chung.walsh05,
0423 author = {Chung, Kai Lai and Walsh, John B.},
0424 pages = {xii+431},
0425 publisher = {Springer-Verlag},
0426 title = {{Markov processes, {B}rownian motion, and time symmetry}},
0427 year = {2005}
0428 }
0429 @article{Maas2011,
0430 archivePrefix = {arXiv},
0431 arxivId = {arXiv:1102.5238v1},
0432 author = {Maas, Jan},
0433 eprint = {arXiv:1102.5238v1},
0434 file = {::},
0435 journal = {Journal of Functional Analysis},
0436 keywords = {and phrases,by rubicon subsidy 680-50-0901,entropy,gradient flows,markov chains,nwo,of the netherlands organi-,optimal transportation,sation for scientific research,the author is supported,wasserstein metric},
0437 pages = {1--32},
0438 publisher = {Elsevier},
0439 title = {{Gradient flows of the entropy for finite Markov chains}},
0440 url = {http://www.sciencedirect.com/science/article/pii/S0022123611002278},
0441 year = {2011}
0442 }
0443 @book{courant.hilbert1,
0444 author = {Courant, R. and Hilbert, D.},
0445 publisher = {Interscience Publishers},
0446 title = {{Methods of mathematical physics. {V}ol. {I}}},
0447 year = {1953}
0448 }
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0451 file = {::},
0452 journal = {Indiana University Mathematics Journal},
0453 number = {6},
0454 title = {{Higher multiplicity in the one-dimensional Allen-Cahn action functional}},
0455 url = {http://eprints3.math.sci.hokudai.ac.jp/1660/1/pre821.pdf},
0456 volume = {56},
0457 year = {2007}
0458 }
0459 @article{Iwata1987,
0460 author = {Iwata, K.},
0461 file = {::},
0462 journal = {Probability theory and related fields},
0463 number = {1},
0464 pages = {141--159},
0465 publisher = {Springer},
0466 title = {{An infinite dimensional stochastic differential equation with state space C(R)}},
0467 url = {http://www.springerlink.com/index/G31PM6220370N4X7.pdf},
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0470 }
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0477 month = apr,
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0479 pages = {233--253},
0480 title = {{Spectral Properties of Hypoelliptic Operators}},
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0482 volume = {235},
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0484 }
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0488 journal = {Journal of Mathematical Analysis and Applications},
0489 pages = {297--340},
0490 title = {{Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems}},
0491 url = {http://www.sciencedirect.com/science/article/pii/S0022247X84714296},
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0494 }
0495 @article{Bobrovsky1992,
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0503 url = {http://www.sciencedirect.com/science/article/pii/0304414992901249},
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0511 keywords = {and phrases,cauchy problem,finite differences,first derivatives estimates},
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0514 title = {{First derivatives estimates for finite-difference schemes}},
0515 url = {http://www.ams.org/journals/mcom/2009-78-268/S0025-5718-09-02229-7/S0025-5718-09-02229-7.pdf},
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0533 @article{freidlin85,
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0538 pages = {639--675},
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0544 @article{Mugnai2007,
0545 author = {Mugnai, L. and R\"{o}ger, M.},
0546 file = {::},
0547 journal = {Arxiv preprint arXiv:0704.1954},
0548 keywords = {allen,cahn equation,large deviation theory,motion by mean curvature,sharp interface limits,stochastic partial differential equations},
0549 pages = {45--78},
0550 title = {{The Allen-Cahn action functional in higher dimensions}},
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0553 year = {2007}
0554 }
0555 @article{LLLP11,
0556 archivePrefix = {arXiv},
0557 arxivId = {arXiv:1105.4636v1},
0558 author = {{Le Bris}, Claude and Leli\`{e}vre, Tony and Luskin, M. and Perez, D.},
0559 eprint = {arXiv:1105.4636v1},
0560 file = {::},
0561 journal = {preprint arXiv:1105.4636},
0562 number = {1},
0563 pages = {1--21},
0564 title = {{A mathematical formalization of the parallel replica dynamics}},
0565 url = {http://arxiv.org/abs/1105.4636},
0566 year = {2011}
0567 }
0568 @article{Chen1987,
0569 abstract = {The effect of fluctuations in rate constants on the kinetic behavior of cyclic reacting systems, caused by a fluctuating external parameter, is studied. It is shown (i) that the stochastic properties of the system can be analyzed analytically by using the usual master equation approach when the external parameter is fluctuating with discrete square pulses and (ii) that the system is equivalent to an expanded chemical kinetic system with no fluctuation in rate constants. When applied to a linear four-state cyclic enzyme system, the formalism can be used to prove analytically the finding that an enzyme can extract the free energy from an externally applied fluctuating membrane potential and perform active free energy transduction. The formalism also can be used to assess the asymmetry constraints imposed on the values of the rate constants in order for the model to work.},
0570 author = {Chen, Y D},
0571 file = {::},
0572 issn = {0027-8424},
0573 journal = {Proceedings of the National Academy of Sciences of the United States of America},
0574 keywords = {Biological Transport,Kinetics,Mathematics,Membrane Potentials,Models, Biological,Thermodynamics},
0575 month = feb,
0576 number = {3},
0577 pages = {729--33},
0578 pmid = {3468510},
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0632 file = {::},
0633 journal = {Stochastic Processes and their Applications},
0634 keywords = {compari-,stochastic differential equation,stochastic partial differential equation},
0635 number = {1},
0636 pages = {23--35},
0637 publisher = {Elsevier},
0638 title = {{Comparison theorems for stochastic differential equations in finite and infinite dimensions}},
0639 url = {http://www.sciencedirect.com/science/article/pii/0304414994900558},
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0642 }
0643 @article{Angenent1988,
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0646 journal = {Journal f\"{u}r die reine und angewandte Mathematik (Crelles Journal)},
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0648 pages = {79--96},
0649 publisher = {Walter de Gruyter, Berlin/New York Berlin, New York},
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0654 }
0655 @article{Gyongy1999a,
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0657 doi = {10.1080/17442509908834205},
0658 file = {::},
0659 issn = {1744-2508},
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0662 number = {1},
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0668 }
0669 @book{Mariani2009,
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0671 booktitle = {Probability Theory and Related Fields},
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0677 number = {3-4},
0678 pages = {607--648},
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0680 url = {http://www.springerlink.com/index/10.1007/s00440-009-0218-6},
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0682 year = {2009}
0683 }
0684 @article{Tugaut2011,
0685 author = {Tugaut, Julian},
0686 file = {::},
0687 journal = {Methods},
0688 keywords = {2000 ams subject classifications,and phrases,cation,exit lo-,exit time,granular media equation,interacting particle systems,large deviations,primary 60f10,propagation of chaos,secondary 60j60,self-stabilizing diffusion},
0689 number = {I},
0690 title = {{Exit problem of McKean-Vlasov diffusions in convex landscape}},
0691 url = {http://hal.archives-ouvertes.fr/hal-00628262/},
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0700 @book{olivieri.vares05,
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0703 publisher = {Cambridge University Press},
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0706 }
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0711 pages = {219----255},
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0714 year = {2002}
0715 }
0716 @article{Eckmann2003a,
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0718 doi = {10.1007/s00220-003-0805-9},
0719 file = {::},
0720 issn = {0010-3616},
0721 journal = {Communications in Mathematical Physics},
0722 month = apr,
0723 number = {2},
0724 pages = {233--253},
0725 title = {{Spectral Properties of Hypoelliptic Operators}},
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0727 volume = {235},
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0730 @article{KORV07,
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0732 doi = {10.1002/cpa.20144},
0733 file = {::},
0734 issn = {00103640},
0735 journal = {Communications on Pure and Applied Mathematics},
0736 month = mar,
0737 number = {3},
0738 pages = {393--438},
0739 title = {{Action minimization and sharp-interface limits for the stochastic Allen-Cahn equation}},
0740 url = {http://doi.wiley.com/10.1002/cpa.20144},
0741 volume = {60},
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0743 }
0744 @article{Dalang2008a,
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0746 doi = {10.1007/s00440-008-0150-1},
0747 file = {::},
0748 issn = {0178-8051},
0749 journal = {Probability Theory and Related Fields},
0750 keywords = {2000,60h15,60j45,hitting probabilities,malliavin calculus,mathematics subject classification,noise,primary,secondary,space-time white,stochastic heat equation},
0751 month = apr,
0752 number = {3-4},
0753 pages = {371--427},
0754 title = {{Hitting probabilities for systems of non-linear stochastic heat equations with multiplicative noise}},
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0757 year = {2008}
0758 }
0759 @article{krumhansl97,
0760 author = {Krumhansl, JA},
0761 file = {::},
0762 journal = {Physica D: Nonlinear Phenomena},
0763 keywords = {biology,biophysics,landscapes},
0764 number = {2-4},
0765 pages = {430--435},
0766 publisher = {Elsevier},
0767 title = {{Landscapes in physics and biology: A tourist's impression}},
0768 url = {http://www.sciencedirect.com/science/article/pii/S0167278997001115},
0769 volume = {107},
0770 year = {1997}
0771 }
0772 @article{Bakhtin2005,
0773 author = {Bakhtin, Yuri and Mattingly, Jonathan C.},
0774 file = {::},
0775 journal = {Communications in Contemporary Mathematics},
0776 keywords = {ergodicity,landau,lyapunov functions,memory,stationary solutions,stochastic differential equations,stochastic ginsburg,stochastic navier,stokes equation},
0777 number = {5},
0778 pages = {553--582},
0779 title = {{EQUATIONS WITH MEMORY AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS}},
0780 volume = {7},
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0782 }
0783 @article{Getoor1984,
0784 author = {Getoor, R. K.},
0785 file = {::},
0786 journal = {Probability Theory and Related Fields},
0787 pages = {1--62},
0788 title = {{Naturality, standardness, and weak duality for Markov processes}},
0789 url = {http://www.springerlink.com/index/H72551LJ206PL211.pdf},
0790 volume = {62},
0791 year = {1984}
0792 }
0793 @article{Hairer2012a,
0794 archivePrefix = {arXiv},
0795 arxivId = {arXiv:1202.1775v1},
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0797 eprint = {arXiv:1202.1775v1},
0798 file = {::},
0799 journal = {Arxiv preprint arXiv:1202.1775},
0800 number = {v},
0801 pages = {1--40},
0802 title = {{Stochastic PDEs with multiscale structure}},
0803 url = {http://arxiv.org/abs/1202.1775},
0804 volume = {2},
0805 year = {2012}
0806 }
0807 @article{Burghelea1992c,
0808 author = {Burghelea, D. and Friedlander, L. and Kappeler, T.},
0809 file = {::},
0810 journal = {Journal of functional analysis},
0811 number = {1},
0812 pages = {34--65},
0813 publisher = {Elsevier},
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0815 url = {http://www.sciencedirect.com/science/article/pii/0022123692900995},
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0818 }
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0822 file = {::},
0823 issn = {0022-4715},
0824 journal = {Journal of Statistical Physics},
0825 keywords = {1 introduction and main,7,dynamical,extensively studied randomly perturbed,homogenization,hypocoercivity,hypoelliptic diffusion,last several decades,one of the most,over the,random perturbations of dynamical,results,subject of intense study,systems has been the},
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0838 keywords = {capacity,diffusion processes,exit times,metastability,potential theory},
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0850 eprint = {arXiv:0901.0039v1},
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0852 journal = {Arxiv preprint arXiv:0901.0039},
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0861 booktitle = {mathweb.unizh.ch},
0862 file = {::},
0863 keywords = {1 institut fuer angewandte,60j10,60k35,ams subject classification,eigenvalue problem,irreversibility,itive reccurence,markov chains,mathematik,metastability,pos-,principal eigenvalue,relaxation time,uncertainty principle,universit},
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0865 title = {{THE LOW LYING SPECTRUM OF IRREVERSIBLE, INFINITE STATE MARKOV CHAINS IN THE METASTABLE REGIME}},
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0871 file = {::},
0872 issn = {03784371},
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0874 keywords = {knot theory,random walks,tie knots,topology},
0875 month = feb,
0876 number = {1-2},
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0881 year = {2000}
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0886 file = {::},
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0888 journal = {The Annals of Probability},
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0890 number = {3},
0891 pages = {896--930},
0892 title = {{Exit from a basin of attraction for stochastic weakly damped nonlinear Schr\"{o}dinger equations}},
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0902 file = {::},
0903 journal = {Stochastic Processes and their Applications},
0904 keywords = {and phrases,fractional brownian motion,malliavin,second order sdes,young integration},
0905 pages = {1--35},
0906 publisher = {Elsevier},
0907 title = {{Pathwise definition of second-order SDEs}},
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0915 eprint = {arXiv:1012.5274v1},
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0927 eprint = {9406140v1},
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0932 primaryClass = {arXiv:hep-th},
0933 publisher = {Birkh\"{a}user},
0934 title = {{Geometry of determinants of elliptic operators}},
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0938 }
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0975 file = {::},
0976 issn = {0178-8051},
0977 journal = {Probability Theory and Related Fields},
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0988 file = {::},
0989 journal = {Physica D: Nonlinear Phenomena},
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0991 number = {3-4},
0992 pages = {227--240},
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0994 title = {{Self-induced stochastic resonance in excitable systems}},
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1008 year = {1986}
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1012 file = {::},
1013 journal = {Math. Comp},
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1015 pages = {973--979},
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1021 @article{Novick-Cohen2000,
1022 author = {Novick-Cohen, Amy},
1023 file = {::},
1024 journal = {Physica D: Nonlinear Phenomena},
1025 keywords = {allen,cahn,curvature,diffuse interface models,geometric motion,grain boundary grooving in,hilliard equations,krzanowski instabilities,motion by mean,motion by minus the,phase transitions,polycrystalline films,sintering,surface diffusion,surface laplacian of mean,triple-junction motion},
1026 number = {1-2},
1027 pages = {1--24},
1028 publisher = {Elsevier},
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1619 archivePrefix = {arXiv},
1620 arxivId = {arXiv:1201.3089v1},
1621 author = {Hairer, M and Ryser, M.D. and Weber, H},
1622 eprint = {arXiv:1201.3089v1},
1623 file = {::},
1624 journal = {Arxiv preprint arXiv:1201.3089},
1625 pages = {1--17},
1626 title = {{Triviality of the 2D stochastic Allen-Cahn equation}},
1627 url = {http://arxiv.org/abs/1201.3089},
1628 year = {2012}
1629 }
1630 @article{Aloupis2012,
1631 archivePrefix = {arXiv},
1632 arxivId = {arXiv:1203.1895v1},
1633 author = {Aloupis, Greg and Demaine, ED},
1634 eprint = {arXiv:1203.1895v1},
1635 file = {::},
1636 journal = {Arxiv preprint arXiv:1203.1895},
1637 pages = {1--21},
1638 title = {{Classic Nintendo Games are (NP-) Hard}},
1639 url = {http://arxiv.org/abs/1203.1895},
1640 year = {2012}
1641 }
1642 @article{Nagasawa1989,
1643 author = {Nagasawa, M.},
1644 file = {::},
1645 journal = {Probability Theory and Related Fields},
1646 number = {1},
1647 pages = {109--136},
1648 publisher = {Springer},
1649 title = {{Transformations of diffusion and Schr\"{o}dinger processes}},
1650 url = {http://www.springerlink.com/index/m572784761tv6566.pdf},
1651 volume = {82},
1652 year = {1989}
1653 }
1654 @article{Berglund2007b,
1655 archivePrefix = {arXiv},
1656 arxivId = {arXiv:math/0611648v2},
1657 author = {Berglund, Nils and Fernandez, Bastien and Gentz, Barbara},
1658 eprint = {0611648v2},
1659 file = {::},
1660 journal = {Nonlinearity},
1661 keywords = {and phrases,chronisation,diffusive coupling,ginzburg,interacting diffusions,landau spde,large deviations,lattice dynamical systems,metastability,most probable transition paths,open systems,spatially extended systems,stochastic differential equations,symmetry groups,symplectic twist maps,syn-,transitions times,wentzell-freidlin theory},
1662 pages = {2583},
1663 primaryClass = {arXiv:math},
1664 publisher = {IOP Publishing},
1665 title = {{Metastability in interacting nonlinear stochastic differential equations: II. Large-N behaviour}},
1666 url = {http://iopscience.iop.org/0951-7715/20/11/007},
1667 volume = {20},
1668 year = {2007}
1669 }
1670 @book{rogers.williams1,
1671 author = {Rogers, L. C. G. and Williams, David},
1672 pages = {xx+386},
1673 publisher = {Cambridge University Press},
1674 title = {{Diffusions, {M}arkov processes, and martingales. {V}ol. 1}},
1675 year = {2000}
1676 }
1677 @article{Wakasa2006,
1678 author = {Wakasa, Tohru},
1679 file = {::},
1680 journal = {Funkcialaj Ekvacioj},
1681 keywords = {2000 mathematics subject classification,34a05,34b05,34b15,35k57,and phrases,chafee-infante problem,eigenfunction,eigenvalue,linearized eigenvalue problem,linearized stability,numbers},
1682 number = {2},
1683 pages = {321--336},
1684 publisher = {J-STAGE},
1685 title = {{Exact Eigenvalues and Eigenfunctions Associated with Linearization for Chafee-Infante Problem}},
1686 url = {http://joi.jlc.jst.go.jp/JST.JSTAGE/fesi/49.321?from=Google},
1687 volume = {49},
1688 year = {2006}
1689 }
1690 @article{Herrmann2005,
1691 author = {Herrmann, Samuel and Imkeller, Peter and Pavlyukevich, Ilya},
1692 file = {::},
1693 journal = {Interacting stochastic systems},
1694 pages = {327--351},
1695 publisher = {Springer},
1696 title = {{Two mathematical approaches to stochastic resonance}},
1697 url = {http://www.springerlink.com/index/h31668u042331923.pdf},
1698 year = {2005}
1699 }
1700 @article{Simon2000,
1701 author = {Simon, Barry},
1702 doi = {10.1006/jfan.2000.3669},
1703 file = {::},
1704 issn = {00221236},
1705 journal = {Journal of Functional Analysis},
1706 month = dec,
1707 number = {2},
1708 pages = {396--420},
1709 title = {{Resonances in One Dimension and Fredholm Determinants}},
1710 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123600936693},
1711 volume = {178},
1712 year = {2000}
1713 }
1714 @article{Hunt1956,
1715 author = {Hunt, GA},
1716 file = {::},
1717 journal = {Proceedings of the National Academy of Sciences of the United States of America},
1718 number = {7},
1719 pages = {414},
1720 publisher = {National Academy of Sciences},
1721 title = {{Markoff processes and potentials}},
1722 url = {http://www.ncbi.nlm.nih.gov/pmc/articles/PMC534239/},
1723 volume = {42},
1724 year = {1956}
1725 }
1726 @article{Baker1981,
1727 author = {Baker, G.A. and Kincaid, J.M.},
1728 file = {::},
1729 journal = {Journal of Statistical Physics},
1730 keywords = {and integral approximants,boson field theory,group,high-temperature series expansions,hyperscaling relations,ising ferromagnet,pade,renormalization},
1731 number = {3},
1732 pages = {469--528},
1733 publisher = {Springer},
1734 title = {{The continuous-spin Ising model, $g_0\varphi^d$ field theory, and the renormalization group}},
1735 url = {http://www.springerlink.com/index/X24187727K254K13.pdf},
1736 volume = {24},
1737 year = {1981}
1738 }
1739 @article{Seeley1969a,
1740 author = {Seeley, R.},
1741 file = {::},
1742 journal = {American Journal of Mathematics},
1743 number = {4},
1744 pages = {889--920},
1745 publisher = {JSTOR},
1746 title = {{The resolvent of an elliptic boundary problem}},
1747 url = {http://www.jstor.org/stable/10.2307/2373309},
1748 volume = {91},
1749 year = {1969}
1750 }
1751 @article{Eckmann2001,
1752 author = {Eckmann, J-p J.-P. and Hairer, Martin},
1753 file = {::},
1754 journal = {Nonlinearity},
1755 pages = {133},
1756 publisher = {IOP Publishing},
1757 title = {{Invariant measures for stochastic partial differential equations in unbounded domains}},
1758 url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.35.5412&rep=rep1&type=pdf http://iopscience.iop.org/0951-7715/14/1/308},
1759 volume = {14},
1760 year = {2001}
1761 }
1762 @article{Gentil2008,
1763 author = {Gentil, Ivan and Imbert, Cyril},
1764 file = {::},
1765 journal = {Asymptotic Analysis},
1766 keywords = {35k15,46n20,47g20,en-,evy operator,fokker-planck equation,fractional laplacian,l,logarithmic sobolev inequalities,mathematics subject classification,tropy production method,$\phi$-entropy inequalities},
1767 number = {3-4},
1768 pages = {125--138},
1769 title = {{The L\'{e}vy-Fokker-Planck equation: {$\Phi$}-entropies and convergence to equilibrium}},
1770 volume = {59},
1771 year = {2008}
1772 }
1773 @article{Majda2006,
1774 author = {Majda, Andrew J. and Timofeyev, Ilya and Vanden-Eijnden, Eric},
1775 doi = {10.1088/0951-7715/19/4/001},
1776 file = {::},
1777 issn = {0951-7715},
1778 journal = {Nonlinearity},
1779 month = apr,
1780 number = {4},
1781 pages = {769--794},
1782 title = {{Stochastic models for selected slow variables in large deterministic systems}},
1783 url = {http://stacks.iop.org/0951-7715/19/i=4/a=001?key=crossref.ac178c9a4b256b0101f4148050ad41f7},
1784 volume = {19},
1785 year = {2006}
1786 }
1787 @article{Albeverio1991,
1788 author = {Albeverio, Sergio and R\"{o}ckner, Michael},
1789 file = {::},
1790 journal = {Probability theory and related fields},
1791 pages = {347--386},
1792 title = {{Stochastic differential equations in infinite dimensions: solutions via Dirichlet forms}},
1793 url = {http://www.springerlink.com/index/w64p2525214u3n11.pdf},
1794 volume = {89},
1795 year = {1991}
1796 }
1797 @article{Hairer2002,
1798 author = {Hairer, Martin},
1799 file = {::},
1800 journal = {Probability theory and related fields},
1801 number = {3},
1802 pages = {345--380},
1803 publisher = {Springer},
1804 title = {{Exponential mixing properties of stochastic PDEs through asymptotic coupling}},
1805 url = {http://www.springerlink.com/index/1xjcv1vvm7lhfj0c.pdf},
1806 volume = {124},
1807 year = {2002}
1808 }
1809 @book{comets.meyre06,
1810 address = {Paris},
1811 author = {Comets, Francis and Meyre, Thierry},
1812 pages = {xii+324},
1813 publisher = {Dunod},
1814 title = {{Calcul stochastique et mod{\`e}les de diffusions}},
1815 year = {2006}
1816 }
1817 @article{bianchi.gaudilliere11,
1818 archivePrefix = {arXiv},
1819 arxivId = {arXiv:1103.1143v1},
1820 author = {Bianchi, Alessandra and Gaudilli\`{e}re, Alexandre},
1821 eprint = {arXiv:1103.1143v1},
1822 file = {::},
1823 journal = {Arxiv preprint arXiv:1103.1143},
1824 pages = {1--32},
1825 title = {{Metastable states, quasi-stationary and soft measures, mixing time asymprtotics via variational principles}},
1826 url = {http://arxiv.org/abs/1103.1143},
1827 year = {2011}
1828 }
1829 @article{Anderssen1984a,
1830 author = {Anderssen, RS and {De Hoog}, FR},
1831 file = {::},
1832 journal = {BIT Numerical Mathematics},
1833 number = {4},
1834 pages = {401--412},
1835 publisher = {Springer},
1836 title = {{On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions}},
1837 url = {http://www.springerlink.com/index/Q75534227QJ860V6.pdf},
1838 volume = {24},
1839 year = {1984}
1840 }
1841 @article{BEGK01,
1842 author = {Bovier, A. and Eckhoff, M. and Gayrard, V. and Klein, M.},
1843 journal = {Probab. Theory Related Fields},
1844 number = {1},
1845 pages = {99----161},
1846 title = {{Metastability in stochastic dynamics of disordered mean-field models}},
1847 volume = {119},
1848 year = {2001}
1849 }
1850 @article{polacik87,
1851 author = {Pol\'{a}cik, P.},
1852 file = {::},
1853 journal = {Nonlinear analysis},
1854 keywords = {and phrases,reaction-diffusion},
1855 number = {5},
1856 pages = {593--597},
1857 publisher = {Elsevier},
1858 title = {{Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions}},
1859 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=8275177},
1860 volume = {11},
1861 year = {1987}
1862 }
1863 @phdthesis{Chapuy,
1864 author = {Chapuy, Guillaume},
1865 file = {::},
1866 title = {{Combinatoire bijective des cartes de genre sup\'{e}rieur}}
1867 }
1868 @article{Cahn1958,
1869 author = {Cahn, John W. and Hilliard, John E.},
1870 doi = {10.1063/1.1744102},
1871 file = {::},
1872 issn = {00219606},
1873 journal = {The Journal of Chemical Physics},
1874 number = {2},
1875 pages = {258},
1876 title = {{Free Energy of a Nonuniform System. I. Interfacial Free Energy}},
1877 url = {http://link.aip.org/link/JCPSA6/v28/i2/p258/s1&Agg=doi},
1878 volume = {28},
1879 year = {1958}
1880 }
1881 @article{levin98,
1882 author = {Levin, S.A.},
1883 file = {::},
1884 journal = {Ecosystems},
1885 keywords = {complex adap-,functional group,gaia,homeostasis,keystone,nonlinearity,self-organization,species,tive system},
1886 number = {5},
1887 pages = {431--436},
1888 publisher = {Springer},
1889 title = {{Ecosystems and the biosphere as complex adaptive systems}},
1890 url = {http://www.springerlink.com/index/VKNT5TK0BCPFC7X1.pdf},
1891 volume = {1},
1892 year = {1998}
1893 }
1894 @article{Berglund2001,
1895 archivePrefix = {arXiv},
1896 arxivId = {arXiv:math/0111178v1},
1897 author = {Berglund, Nils},
1898 eprint = {0111178v1},
1899 file = {::;::},
1900 journal = {Arxiv preprint math/0111178},
1901 primaryClass = {arXiv:math},
1902 title = {{Perturbation theory of dynamical systems}},
1903 url = {http://arxiv.org/abs/math/0111178},
1904 year = {2001}
1905 }
1906 @article{Funaki2006,
1907 author = {Funaki, Tadahisa and Kikuchi, Masashi and Potthoff, J\"{u}rgen},
1908 file = {::},
1909 journal = {Preprint},
1910 keywords = {60g17,60g60,60h15,ams subject classification,direction-dependent modulus of continuity,dom fields,garsia-rodemich-rumsey lemma,kolmogorov- centsov,ran-,sample continuity,theorem},
1911 pages = {1--13},
1912 title = {{Direction-dependent modulus of continuity for random fields}},
1913 url = {http://www.ms.u-tokyo.ac.jp/$\sim$funaki/publ/Fu-Ki-Pott.pdf},
1914 year = {2006}
1915 }
1916 @article{Kohn2006,
1917 author = {Kohn, Robert V. and Reznikoff, Maria G. and Tonegawa, Yoshihiro},
1918 doi = {10.1007/s00526-005-0370-5},
1919 file = {::},
1920 issn = {0944-2669},
1921 journal = {Calculus of Variations and Partial Differential Equations},
1922 keywords = {action minimization,allen-cahn equation,gamma,large deviation theory,sharp-interface limits,stochastic partial differential equations},
1923 month = feb,
1924 number = {4},
1925 pages = {503--534},
1926 title = {{Sharp-interface limit of the Allen-Cahn action functional in one space dimension}},
1927 url = {http://www.springerlink.com/index/10.1007/s00526-005-0370-5},
1928 volume = {25},
1929 year = {2006}
1930 }
1931 @article{Faierman1972,
1932 author = {Faierman, M.},
1933 file = {::},
1934 journal = {Journal of Differential Equations},
1935 pages = {10--37},
1936 title = {{An oscillation theorem for a one-parameter ordinary differential equation of the second order}},
1937 url = {http://adsabs.harvard.edu/abs/1972JDE....11...10F},
1938 volume = {11},
1939 year = {1972}
1940 }
1941 @article{Getoor1986,
1942 author = {Getoor, R. K. and Steffens, J.},
1943 file = {::},
1944 journal = {Probability theory and related fields},
1945 pages = {415--445},
1946 title = {{Capacity theory without duality}},
1947 url = {http://www.springerlink.com/index/P2JVQ45X61274830.pdf},
1948 volume = {73},
1949 year = {1986}
1950 }
1951 @article{Allman2009,
1952 author = {Allman, Michael and Betz, Volker},
1953 doi = {10.1016/j.spa.2009.01.007},
1954 file = {::},
1955 issn = {03044149},
1956 journal = {Stochastic Processes and their Applications},
1957 keywords = {asymptotic theory,first-exit from space,interacting brownian particles,time domains},
1958 month = aug,
1959 number = {8},
1960 pages = {2645--2659},
1961 publisher = {Elsevier B.V.},
1962 title = {{Breaking the chain}},
1963 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414909000283},
1964 volume = {119},
1965 year = {2009}
1966 }
1967 @article{gyongy.pardoux93a,
1968 author = {Gy\"{o}ngy, Istv\'{a}n and Pardoux, Etienne},
1969 file = {::},
1970 journal = {Probability theory and related fields},
1971 pages = {211--229},
1972 title = {{On the regularization effect of space-time white noise on quasi-linear parabolic partial differential equations}},
1973 url = {http://www.springerlink.com/index/j7523u2h87384792.pdf},
1974 volume = {97},
1975 year = {1993}
1976 }
1977 @article{fiedler.rocha10,
1978 author = {Fiedler, Bernold and Rocha, Carlos},
1979 doi = {10.1515/CRELLE.2009.076},
1980 file = {::},
1981 journal = {Journal of Dynamics and Differential Equations},
1982 number = {2},
1983 pages = {121--162},
1984 publisher = {Springer},
1985 title = {{Connectivity and design of planar global attractors of Sturm type. III: Small and Platonic examples}},
1986 url = {http://www.springerlink.com/index/e1867pl607792418.pdf},
1987 volume = {22},
1988 year = {2010}
1989 }
1990 @article{Fukushima2004,
1991 author = {Fukushima, Masatoshi and He, Ping and Ying, Jiangang},
1992 doi = {10.1214/009117904000000649},
1993 file = {::},
1994 issn = {0091-1798},
1995 journal = {The Annals of Probability},
1996 month = oct,
1997 number = {4},
1998 pages = {3138--3166},
1999 title = {{Time changes of symmetric diffusions and Feller measures}},
2000 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1107883349/},
2001 volume = {32},
2002 year = {2004}
2003 }
2004 @article{El-Gendi1969,
2005 author = {El-Gendi, SE},
2006 file = {::},
2007 journal = {The Computer Journal},
2008 number = {3},
2009 pages = {282--287},
2010 publisher = {Br Computer Soc},
2011 title = {{Chebyshev solution of differential, integral and integro-differential equations}},
2012 url = {http://comjnl.oxfordjournals.org/content/12/3/282.short},
2013 volume = {12},
2014 year = {1969}
2015 }
2016 @book{kunita,
2017 author = {Kunita, Hiroshi},
2018 edition = {{re\-print}},
2019 pages = {xiv+346},
2020 publisher = {Cambridge University Press},
2021 title = {{Stochastic flows and stochastic differential equations}},
2022 year = {1997}
2023 }
2024 @article{eckhoff05,
2025 author = {Eckhoff, Michael},
2026 doi = {10.1214/009117904000000991},
2027 file = {::},
2028 issn = {0091-1798},
2029 journal = {The Annals of Probability},
2030 month = jan,
2031 number = {1},
2032 pages = {244--299},
2033 title = {{Precise asymptotics of small eigenvalues of reversible diffusions in the metastable regime}},
2034 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1108141727/},
2035 volume = {33},
2036 year = {2005}
2037 }
2038 @article{Reddien1976,
2039 author = {Reddien, GW},
2040 file = {::},
2041 journal = {Math. Comp},
2042 number = {134},
2043 pages = {278--282},
2044 title = {{Finite-Difference Approximation to Singular Sturm-Liouville Eigenvalue Problems}},
2045 url = {http://www.ams.org/journals/mcom/1976-30-134/S0025-5718-1976-0403235-1/S0025-5718-1976-0403235-1.pdf},
2046 volume = {30},
2047 year = {1976}
2048 }
2049 @article{Barnett1925,
2050 author = {Barnett, IA},
2051 file = {::},
2052 journal = {Bull. Amer. Math. Soc},
2053 pages = {263--265},
2054 title = {{Integro-differential equations}},
2055 url = {http://www.ams.org/bull/1925-31-05/S0002-9904-1925-04048-3/S0002-9904-1925-04048-3.pdf},
2056 year = {1925}
2057 }
2058 @article{Lesch1998a,
2059 archivePrefix = {arXiv},
2060 arxivId = {arXiv:math/9902114v1},
2061 author = {Lesch, Matthias},
2062 eprint = {9902114v1},
2063 file = {::},
2064 journal = {Mathematische Nachrichten},
2065 keywords = {and phrases,determinants,liouville theory,sturm},
2066 number = {1},
2067 pages = {139--170},
2068 primaryClass = {arXiv:math},
2069 publisher = {Wiley Online Library},
2070 title = {{Determinants of Regular Singular Sturm-Liouville Operators}},
2071 url = {http://onlinelibrary.wiley.com/doi/10.1002/mana.19981940110/abstract},
2072 volume = {194},
2073 year = {1998}
2074 }
2075 @article{Gyongy1998,
2076 author = {Gy\"{o}ngy, Istv\'{a}n},
2077 file = {::},
2078 journal = {Stochastic Processes and their Applications},
2079 pages = {271--299},
2080 title = {{Existence and uniqueness results for semilinear stochastic partial differential equations}},
2081 url = {http://www.sciencedirect.com/science/article/pii/S0304414997001038},
2082 volume = {73},
2083 year = {1998}
2084 }
2085 @article{meleard.villemonais11,
2086 abstract = {This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes when 0 is an absorbing point almost surely attained by the process. The hitting time of this point, namely the extinction time, can be large compared to the physical time and the population size can fluctuate for large amount of time before extinction actually occurs. This phenomenon can be understood by the study of quasi-limiting distributions. In this paper, general results on quasi-stationarity are given and examples developed in detail. One shows in particular how this notion is related to the spectral properties of the semi-group of the process killed at 0. Then we study different stochastic population models including nonlinear terms modeling the regulation of the population. These models will take values in countable sets (as birth and death processes) or in continuous spaces (as logistic Feller diffusion processes or stochastic Lotka-Volterra processes). In all these situations we study in detail the quasi-stationarity properties. We also develop an algorithm based on Fleming-Viot particle systems and show a lot of numerical pictures.},
2087 archivePrefix = {arXiv},
2088 arxivId = {1112.4732},
2089 author = {M\'{e}l\'{e}ard, Sylvie and Villemonais, Denis},
2090 eprint = {1112.4732},
2091 month = dec,
2092 title = {{Quasi-stationary distributions and population processes}},
2093 url = {http://arxiv.org/abs/1112.4732},
2094 year = {2011}
2095 }
2096 @article{MOS90,
2097 author = {Martinelli, Fabio and Olivieri, Enzo and Scoppola, Elisabetta},
2098 file = {::},
2099 journal = {Journal of statistical physics},
2100 keywords = {1,for some,glauber dynamics,in this paper we,introduction a n d,ising model,m a i n,metastability,prove a result on,result,the convergence to equilibrium},
2101 number = {5},
2102 pages = {1105--1119},
2103 publisher = {Springer},
2104 title = {{Metastability and exponential approach to equilibrium for low-temperature stochastic Ising models}},
2105 url = {http://www.springerlink.com/index/u43216617w08xh17.pdf},
2106 volume = {61},
2107 year = {1990}
2108 }
2109 @article{eyring35,
2110 author = {Eyring, H},
2111 file = {::},
2112 journal = {The Journal of Chemical Physics},
2113 title = {{The activated complex in chemical reactions}},
2114 url = {http://link.aip.org/link/?jcp/3/107},
2115 volume = {3},
2116 year = {1935}
2117 }
2118 @techreport{Bovier2009,
2119 author = {Bovier, Anton},
2120 booktitle = {Spin Glasses: Statics and Dynamics},
2121 file = {::},
2122 pages = {40},
2123 publisher = {Springer},
2124 title = {{A Short Course on Mean Field Spin Glasses}},
2125 url = {http://www.springerlink.com/index/R571857J605253X0.pdf},
2126 year = {2009}
2127 }
2128 @article{Theory2009,
2129 author = {Camilli, Fabio and Cesaroni, Annalisa},
2130 file = {::},
2131 journal = {Journal of Dynamical Systems},
2132 keywords = {and phrases,large deviations,pde aubry-mather theory,random perturbations of dynamical,systems,tions,viscosity solu-},
2133 pages = {1--28},
2134 title = {{Randomly perturbed dynamical systems and Aubry-Mather theory}},
2135 url = {http://inderscience.metapress.com/index/e145361275746ku6.pdf},
2136 year = {2009}
2137 }
2138 @article{bouchaud.mezard97,
2139 author = {Bouchaud, J.P. and M\'{e}zard, Marc},
2140 file = {::},
2141 journal = {Physica D: Nonlinear Phenomena},
2142 keywords = {1,and for applications,difficulties common to disordered,elastic manifolds,i n t r,importance both from a,impurities is of fundamental,many of the specific,o d u c,objects pinned by random,point of view,randomness,renormalisation,systems are at stake,t i o n,the,the physics of elastic,theoretical},
2143 number = {2-4},
2144 pages = {174--182},
2145 publisher = {Elsevier},
2146 title = {{Landscape approach for pinned elastic interfaces}},
2147 url = {http://www.sciencedirect.com/science/article/pii/S0167278997000845},
2148 volume = {107},
2149 year = {1997}
2150 }
2151 @article{Debussche2009,
2152 author = {Debussche, Arnaud and Printems, Jacques},
2153 file = {::},
2154 journal = {Math. Comp},
2155 keywords = {28 years from publication,and phrases,c 2008 american mathematical,euler scheme,finite element,reverts to public domain,society,stochastic heat equation,weak order},
2156 number = {266},
2157 pages = {845--863},
2158 title = {{Weak order for the discretization of the stochastic heat equation}},
2159 url = {http://www.ams.org/mcom/2009-78-266/S0025-5718-08-02184-4/S0025-5718-08-02184-4.pdf},
2160 volume = {78},
2161 year = {2009}
2162 }
2163 @article{barret12,
2164 author = {Barret, Florent},
2165 institution = {CMAP},
2166 journal = {pr\'{e}publication CMAP, soumis.},
2167 title = {{Sharp asymptotics of metastable transition times for one dimensional SPDEs}},
2168 year = {2012}
2169 }
2170 @article{wolfrum02,
2171 author = {Wolfrum, Matthias},
2172 doi = {10.1006/jdeq.2001.4114},
2173 file = {::},
2174 issn = {00220396},
2175 journal = {Journal of Differential Equations},
2176 keywords = {attractors,heteroclinic connections,nodal properties,order structures,scalar semilinear parabolic pde},
2177 month = jul,
2178 number = {1},
2179 pages = {56--78},
2180 title = {{A Sequence of Order Relations: Encoding Heteroclinic Connections in Scalar Parabolic PDE}},
2181 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039601941142},
2182 volume = {183},
2183 year = {2002}
2184 }
2185 @article{IP08,
2186 author = {Imkeller, Peter and Pavlyukevich, Ilya},
2187 doi = {10.1051/ps},
2188 file = {::},
2189 journal = {{\\ ESAIM: Probability and Statistics}},
2190 keywords = {and phrases,evy process,extreme events,first exit time,heavy tail,jump diffusion,l,metastability,regular variation},
2191 number = {July},
2192 pages = {412--437},
2193 title = {{Metastable Behaviour of Small Noise Levy-Driven Diffusion}},
2194 url = {http://cdsweb.cern.ch/record/926151},
2195 volume = {12},
2196 year = {2008}
2197 }
2198 @book{Cerrai2001,
2199 author = {Cerrai, Sandra},
2200 booktitle = {Lecture Notes in Mathematics},
2201 file = {::},
2202 isbn = {354042136X},
2203 pages = {329},
2204 title = {{Second order PDEs in finite and infinite dimension}},
2205 year = {2001}
2206 }
2207 @article{DaPrato1996,
2208 author = {{Da Prato}, Giuseppe and Debussche, Arnaud},
2209 file = {::},
2210 journal = {Nonlinear Analysis: Theory, Methods \& Applications},
2211 keywords = {and phrases,stochastic equations,white noise},
2212 number = {2},
2213 pages = {241--263},
2214 title = {{Stochastic Cahn-Hilliard equation}},
2215 url = {http://www.newton.ac.uk/programmes/SPD/seminars/063010101.pdf},
2216 volume = {26},
2217 year = {1996}
2218 }
2219 @article{KKR93,
2220 author = {Kavian, Otared and Kerkyacharian, G\'{e}rard and Roynette, Bernard},
2221 file = {::},
2222 journal = {Journal of functional analysis},
2223 pages = {155--196},
2224 title = {{Quelques remarques sur l'ultracontractivit\'{e}}},
2225 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=4642605},
2226 volume = {111},
2227 year = {1993}
2228 }
2229 @article{BFG07b,
2230 archivePrefix = {arXiv},
2231 arxivId = {arXiv:math/0611648v2},
2232 author = {Berglund, Nils and Fernandez, Bastien and Gentz, Barbara},
2233 eprint = {0611648v2},
2234 file = {::},
2235 journal = {Nonlinearity},
2236 keywords = {and phrases,chronisation,diffusive coupling,ginzburg,interacting diffusions,landau spde,large deviations,lattice dynamical systems,metastability,most probable transition,most probable transition paths,open systems,paths,spatially extended systems,stochastic differential equations,symmetry groups,symplectic twist maps,syn-,synchronisation,transitions times,wentzell-freidlin theory},
2237 pages = {2583},
2238 primaryClass = {arXiv:math},
2239 publisher = {IOP Publishing},
2240 title = {{Metastability in interacting nonlinear stochastic differential equations: II. Large-N behaviour}},
2241 url = {http://iopscience.iop.org/0951-7715/20/11/006 http://iopscience.iop.org/0951-7715/20/11/007},
2242 volume = {20},
2243 year = {2007}
2244 }
2245 @article{Kuttler1970,
2246 author = {Kuttler, J.R.},
2247 file = {::},
2248 journal = {SIAM Journal on Numerical Analysis},
2249 number = {2},
2250 pages = {206--232},
2251 publisher = {JSTOR},
2252 title = {{Finite difference approximations for eigenvalues of uniformly elliptic operators}},
2253 url = {http://www.jstor.org/stable/10.2307/2949456},
2254 volume = {7},
2255 year = {1970}
2256 }
2257 @article{Gyongy2001,
2258 author = {Gy\"{o}ngy, Istv\'{a}n and Martinez, Teresa},
2259 file = {::},
2260 journal = {Czechoslovak Mathematical Journal},
2261 keywords = {krylov,s estimate,stochastic differential equations},
2262 number = {4},
2263 pages = {763--783},
2264 publisher = {Springer},
2265 title = {{On stochastic differential equations with locally unbounded drift}},
2266 url = {http://www.springerlink.com/index/HG25TU50XWHJ1775.pdf},
2267 volume = {51},
2268 year = {2001}
2269 }
2270 @incollection{Holden2010,
2271 author = {Holden, Helge and Oksendal, Bernt and Uboe, Jan and Zhang, Tusheng},
2272 booktitle = {Stochastic partial differential equations},
2273 file = {::},
2274 title = {{Stochastic partial differential equations, frontmatter}},
2275 url = {http://www.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=A8325264AH},
2276 year = {2010}
2277 }
2278 @article{Adams2010,
2279 archivePrefix = {arXiv},
2280 arxivId = {arXiv:1004.4076v1},
2281 author = {Adams, Stefan and Dirr, Nicolas and Peletier, M.A. and Zimmer, Johannes},
2282 eprint = {arXiv:1004.4076v1},
2283 file = {::},
2284 journal = {Communications in Mathematical Physics},
2285 keywords = {and phrases,gamma-convergence,generalized gradient flows,hydrodynamic limits,optimal transport,stochastic particle systems,tional evolution equations,varia-},
2286 number = {2},
2287 pages = {1--25},
2288 publisher = {Springer},
2289 title = {{From a large-deviations principle to the Wasserstein gradient flow: A new micro-macro passage}},
2290 url = {http://www.springerlink.com/index/C5176KX3T224N276.pdf},
2291 year = {2010}
2292 }
2293 @article{HKN04,
2294 author = {Helffer, Bernard and Klein, Markus and Nier, Francis},
2295 journal = {Mat. Contemp.},
2296 pages = {41--85},
2297 title = {{Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach}},
2298 url = {http://hal.archives-ouvertes.fr/inria-00001236/},
2299 volume = {26},
2300 year = {2004}
2301 }
2302 @article{Dreyfus1978,
2303 author = {Dreyfus, Tommy and Dym, Harry},
2304 file = {::},
2305 journal = {Duke Mathematical Journal},
2306 number = {1},
2307 title = {{Product formulas for the eigenvalues of a class of boundary value problems}},
2308 url = {http://projecteuclid.org/euclid.dmj/1077312684},
2309 volume = {45},
2310 year = {1978}
2311 }
2312 @article{Desvillettes2004,
2313 author = {Desvillettes, L. and Villani, C.},
2314 doi = {10.1007/s00222-004-0389-9},
2315 file = {::},
2316 issn = {0020-9910},
2317 journal = {Inventiones mathematicae},
2318 month = sep,
2319 number = {2},
2320 pages = {245--316},
2321 title = {{On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation}},
2322 url = {http://www.springerlink.com/index/10.1007/s00222-004-0389-9},
2323 volume = {159},
2324 year = {2004}
2325 }
2326 @article{Parter1982,
2327 author = {Parter, SV},
2328 file = {::},
2329 journal = {SIAM Journal on Numerical Analysis},
2330 number = {3},
2331 pages = {518--530},
2332 title = {{On the eigenvalues of second order elliptic difference operators}},
2333 url = {http://www.jstor.org/stable/10.2307/2156965},
2334 volume = {19},
2335 year = {1982}
2336 }
2337 @article{BGW11,
2338 archivePrefix = {arXiv},
2339 arxivId = {arXiv:1109.0449v1},
2340 author = {Bodineau, Thierry and Graham, Benjamin and Wouts, Marc},
2341 eprint = {arXiv:1109.0449v1},
2342 file = {::},
2343 journal = {Arxiv preprint arXiv:1109.0449},
2344 title = {{Metastability in the dilute Ising model}},
2345 url = {http://arxiv.org/abs/1109.0449},
2346 year = {2011}
2347 }
2348 @article{CGOV84,
2349 author = {Cassandro, Marzio and Galves, A. and Olivieri, Enzo and Vares, M.E.},
2350 file = {::},
2351 journal = {Journal of statistical physics},
2352 number = {5},
2353 pages = {603--634},
2354 publisher = {Springer},
2355 title = {{Metastable behavior of stochastic dynamics: a pathwise approach}},
2356 url = {http://www.springerlink.com/index/LJ15242528467W34.pdf},
2357 volume = {35},
2358 year = {1984}
2359 }
2360 @article{BdHS10,
2361 author = {Bovier, Anton and den Hollander, Frank and Spitoni, Cristian},
2362 doi = {10.1214/09-AOP492},
2363 file = {::},
2364 issn = {0091-1798},
2365 journal = {The Annals of Probability},
2366 keywords = {and phrases,berman,capacity,critical droplet,dirichlet principle,glauber dynamics,kawasaki dynamics,konsowa principle,last-exit biased distribution,metastable tran-,sition time},
2367 month = mar,
2368 number = {2},
2369 pages = {661--713},
2370 title = {{Homogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures}},
2371 url = {http://projecteuclid.org/euclid.aop/1268143530},
2372 volume = {38},
2373 year = {2010}
2374 }
2375 @article{Funaki1989,
2376 author = {Funaki, Tadahisa},
2377 file = {::},
2378 journal = {Probability Theory and Related Fields},
2379 pages = {39--93},
2380 title = {{Derivation of the hydrodynamical equation for one-dimensional Ginzburg-Landau model}},
2381 url = {http://www.springerlink.com/index/V50502526002212L.pdf},
2382 volume = {82},
2383 year = {1989}
2384 }
2385 @article{Khoshnevisan2008,
2386 author = {Khoshnevisan, Davar and Levin, D. and Mendezhernandez, P.},
2387 doi = {10.1016/j.spa.2007.10.014},
2388 file = {::},
2389 issn = {03044149},
2390 journal = {Stochastic Processes and their Applications},
2391 keywords = {1 5413460987,1 5413465621,a,ac,capacity in wiener space,corresponding author,cr,d,davar,dlevin,e-mail addresses,edu,fax,j,khoshnevisan,kolmogorov entropy,levin,lower functions,m,math,mendez,p,pedro,purdue,tel,ucr,uoregon,utah},
2392 month = oct,
2393 number = {10},
2394 pages = {1723--1737},
2395 title = {{Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov’s $\epsilon$$\epsilon$-entropy}},
2396 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414907001998},
2397 volume = {118},
2398 year = {2008}
2399 }
2400 @article{Bansaye2009,
2401 author = {Bansaye, Vincent},
2402 doi = {10.1016/j.spa.2008.12.005},
2403 file = {::},
2404 issn = {03044149},
2405 journal = {Stochastic Processes and their Applications},
2406 keywords = {bpre,branching process in random,environment,q-process,random walk with,yaglom distribution},
2407 month = aug,
2408 number = {8},
2409 pages = {2436--2464},
2410 publisher = {Elsevier B.V.},
2411 title = {{Surviving particles for subcritical branching processes in random environment}},
2412 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908001890},
2413 volume = {119},
2414 year = {2009}
2415 }
2416 @article{Coskun2005,
2417 author = {Coşkun, Haskız and Bayram, Neslihan},
2418 doi = {10.1016/j.jmaa.2004.10.030},
2419 file = {::},
2420 issn = {0022247X},
2421 journal = {Journal of Mathematical Analysis and Applications},
2422 keywords = {asymptotics,eigenparameter,eigenvalues,liouville problems,sturm},
2423 month = jun,
2424 number = {2},
2425 pages = {548--566},
2426 title = {{Asymptotics of eigenvalues for regular Sturm–Liouville problems with eigenvalue parameter in the boundary condition}},
2427 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022247X04008698},
2428 volume = {306},
2429 year = {2005}
2430 }
2431 @article{Seeley1969,
2432 author = {Seeley, R},
2433 file = {::},
2434 journal = {American Journal of Mathematics},
2435 number = {4},
2436 pages = {889--920},
2437 title = {{The resolvent of an elliptic boundary problem}},
2438 url = {http://www.jstor.org/stable/10.2307/2373309},
2439 volume = {91},
2440 year = {1969}
2441 }
2442 @article{Hausenblas2003,
2443 author = {Hausenblas, Erika},
2444 file = {::},
2445 journal = {Potential Analysis},
2446 keywords = {numerical ap-,stochastic evolution equations,stochastic partial differential equations},
2447 number = {2},
2448 pages = {141--186},
2449 publisher = {Springer},
2450 title = {{Approximation for semilinear stochastic evolution equations}},
2451 url = {http://www.springerlink.com/index/U1242M1273831852.pdf},
2452 volume = {18},
2453 year = {2003}
2454 }
2455 @article{Bogachev2001,
2456 author = {Bogachev, Vladimir I. and Rockner, Michael and Wang, F.Y.},
2457 file = {::},
2458 journal = {Comptes Rendus de l'Academie des Sciences-Serie I-Mathematique},
2459 number = {4},
2460 pages = {333--338},
2461 publisher = {Paris: Gauthier-Villars, c1984-c2001.},
2462 title = {{Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions}},
2463 url = {http://math.bnu.edu.cn/$\sim$wangfy/files/2001_02.pdf},
2464 volume = {332},
2465 year = {2001}
2466 }
2467 @article{Zhou2008,
2468 abstract = {An adaptive minimum action method is proposed for computing the most probable transition paths between stable equilibria in metastable systems that do not necessarily have an underlying energy function, by minimizing the action functional associated with such transition paths. This new algorithm uses the moving mesh strategy to adaptively adjust the grid points over the time interval of transition. Numerical examples are presented to demonstrate the efficiency of the adaptive minimum action method.},
2469 author = {Zhou, Xiang and Ren, Weiqing and E, Weinan},
2470 doi = {10.1063/1.2830717},
2471 file = {::},
2472 issn = {0021-9606},
2473 journal = {The Journal of chemical physics},
2474 month = mar,
2475 number = {10},
2476 pages = {104111},
2477 pmid = {18345881},
2478 title = {{Adaptive minimum action method for the study of rare events.}},
2479 url = {http://www.ncbi.nlm.nih.gov/pubmed/18345881},
2480 volume = {128},
2481 year = {2008}
2482 }
2483 @article{Nualart2009,
2484 author = {Nualart, Eulalia and Viens, Frederi},
2485 doi = {10.1016/j.spa.2008.07.009},
2486 file = {::},
2487 issn = {03044149},
2488 journal = {Stochastic Processes and their Applications},
2489 keywords = {0,1,b h with hurst,circle driven by an,dimensional fractional brownian motion,equations on the unit,fractional brownian motion,hitting probabilities,infinite-,introduction and main results,of d stochastic heat,parameter h,path regularity,stochastic heat equation,that is,we consider a system},
2490 month = may,
2491 number = {5},
2492 pages = {1505--1540},
2493 publisher = {Elsevier B.V.},
2494 title = {{The fractional stochastic heat equation on the circle: Time regularity and potential theory}},
2495 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908001233},
2496 volume = {119},
2497 year = {2009}
2498 }
2499 @article{Vasilach1973,
2500 author = {Vasilach, S.},
2501 file = {::},
2502 journal = {Publications de l'institut math\'{e}matique},
2503 number = {29},
2504 pages = {153--169},
2505 title = {{Solutions of some Parabolic Integro-differential Equations by means of the algebraic operational calculus of distributions}},
2506 volume = {15},
2507 year = {1973}
2508 }
2509 @article{Laetsch1975,
2510 author = {Laetsch, T},
2511 file = {::},
2512 journal = {Indiana University. Math. Journal},
2513 number = {7},
2514 pages = {651--658},
2515 title = {{Critical solutions of autonomous non linear boundary value problems}},
2516 url = {http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:critical+solutions+of+autonomous+nonlinear+boundary+value+problems#8},
2517 volume = {24},
2518 year = {1975}
2519 }
2520 @article{Rinaldi2000,
2521 author = {Rinaldi, Sergio and Scheffer, Marten},
2522 doi = {10.1007/s100210000045},
2523 file = {::},
2524 issn = {1432-9840},
2525 journal = {Ecosystems},
2526 keywords = {bation,bifurcation analysis,catastrophes,fast cycles,fast dynamics,quasi,singular pertur-,slow,steady state},
2527 month = nov,
2528 number = {6},
2529 pages = {507--521},
2530 title = {{Geometric Analysis of Ecological Models with Slow and Fast Processes}},
2531 url = {http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s100210000045},
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2533 year = {2000}
2534 }
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2549 issn = {0002-9947},
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2552 number = {2},
2553 pages = {545--545},
2554 title = {{The dynamics of rotating waves in scalar reaction diffusion equations}},
2555 url = {http://www.ams.org/jourcgi/jour-getitem?pii=S0002-9947-1988-0940217-X},
2556 volume = {307},
2557 year = {1988}
2558 }
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2566 number = {6},
2567 pages = {1397--1440},
2568 publisher = {Elsevier Masson SAS},
2569 title = {{Generic Morse–Smale property for the parabolic equation on the circle}},
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2573 }
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2578 pages = {130--141},
2579 title = {{Deterministic non-periodic flow}},
2580 url = {http://en.scientificcommons.org/19848251},
2581 volume = {20},
2582 year = {1963}
2583 }
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2585 author = {Marcus, R.},
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2588 number = {3},
2589 pages = {275--286},
2590 publisher = {Elsevier},
2591 title = {{Parabolic It\^{o} equations with monotone nonlinearities}},
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2594 year = {1978}
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2598 file = {::},
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2600 number = {4},
2601 pages = {587--603},
2602 publisher = {International Press of Boston},
2603 title = {{Analysis of SPDEs arising in path sampling. Part I: The Gaussian case}},
2604 url = {http://projecteuclid.org/euclid.cms/1144429334},
2605 volume = {3},
2606 year = {2005}
2607 }
2608 @article{gyongy99,
2609 author = {Gy{\"o}ngy, Istv{\'a}n},
2610 journal = {Potential Analysis},
2611 title = {{Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II}},
2612 url = {http://www.springerlink.com/index/X644L10403753878.pdf},
2613 year = {1999}
2614 }
2615 @article{Danchin2011,
2616 abstract = {Many biologists are calling for an 'extended evolutionary synthesis' that would 'modernize the modern synthesis' of evolution. Biological information is typically considered as being transmitted across generations by the DNA sequence alone, but accumulating evidence indicates that both genetic and non-genetic inheritance, and the interactions between them, have important effects on evolutionary outcomes. We review the evidence for such effects of epigenetic, ecological and cultural inheritance and parental effects, and outline methods that quantify the relative contributions of genetic and non-genetic heritability to the transmission of phenotypic variation across generations. These issues have implications for diverse areas, from the question of missing heritability in human complex-trait genetics to the basis of major evolutionary transitions.},
2617 author = {Danchin, Etienne and Charmantier, Anne and Champagne, Frances A. and Mesoudi, Alex and Pujol, Benoit and Blanchet, Simon},
2618 doi = {10.1038/nrg3028},
2619 file = {::},
2620 issn = {1471-0064},
2621 journal = {Nature reviews. Genetics},
2622 month = jan,
2623 number = {7},
2624 pages = {475--86},
2625 pmid = {21681209},
2626 publisher = {Nature Publishing Group},
2627 title = {{Beyond DNA: integrating inclusive inheritance into an extended theory of evolution.}},
2628 url = {http://www.ncbi.nlm.nih.gov/pubmed/21681209},
2629 volume = {12},
2630 year = {2011}
2631 }
2632 @techreport{Blomker2010,
2633 author = {Bl\"{o}mker, D. and Jentzen, Arnulf},
2634 file = {::},
2635 institution = {Working paper},
2636 keywords = {1,35k90,60h15,ams subject classifications,equation,galerkin approximations,in this work we,introduction,present a very general,result for the spa-,stochastic burgers equation,stochastic heat,stochastic partial differential equation,stochastic reaction diffusion equation,strong error criteria},
2637 pages = {1--46},
2638 title = {{Galerkin approximations for the stochastic Burgers equation}},
2639 url = {http://opus.bibliothek.uni-augsburg.de/volltexte/2009/1444/},
2640 year = {2010}
2641 }
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2646 title = {{On last exit times}},
2647 year = {1959}
2648 }
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2654 pages = {43--56},
2655 title = {{ASYMPTOTIC FORMULAS FOR DISCRETE EIGENVALUE}},
2656 volume = {11},
2657 year = {2001}
2658 }
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2660 author = {Jona-Lasinio, G. and Mitter, PK},
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2662 journal = {Communications in Mathematical Physics},
2663 number = {3},
2664 pages = {409--436},
2665 publisher = {Springer},
2666 title = {{On the stochastic quantization of field theory}},
2667 url = {http://www.springerlink.com/index/L1G0588734G0R075.pdf},
2668 volume = {101},
2669 year = {1985}
2670 }
2671 @article{Eckmann2001c,
2672 author = {Eckmann, J.-P. and Hairer, Martin},
2673 file = {::;::;::},
2674 journal = {Nonlinearity},
2675 pages = {133},
2676 publisher = {IOP Publishing},
2677 title = {{Invariant measures for stochastic partial differential equations in unbounded domains}},
2678 url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.35.5412&rep=rep1&type=pdf http://iopscience.iop.org/0951-7715/14/1/308},
2679 volume = {14},
2680 year = {2001}
2681 }
2682 @article{Burghelea1992a,
2683 author = {Burghelea, D. and Friedlander, L. and Kappeler, T.},
2684 file = {::},
2685 journal = {Communications in Mathematical Physics},
2686 number = {2},
2687 pages = {431},
2688 publisher = {Springer},
2689 title = {{Erratum: On the determination of elliptic differential and finite difference operators in vector bundles over $S^1$}},
2690 url = {http://www.springerlink.com/index/k46538n72j561608.pdf},
2691 volume = {150},
2692 year = {1992}
2693 }
2694 @incollection{Grosche1993,
2695 archivePrefix = {arXiv},
2696 arxivId = {arXiv:hep-th/9302097v1},
2697 author = {Grosche, Christian},
2698 booktitle = {Arxiv preprint hep-th/9302097},
2699 eprint = {9302097v1},
2700 file = {::},
2701 number = {November},
2702 primaryClass = {arXiv:hep-th},
2703 title = {{An introduction into the Feynman path integral}},
2704 url = {http://arxiv.org/abs/hep-th/9302097},
2705 year = {1993}
2706 }
2707 @inproceedings{Albeverio2011,
2708 author = {Albeverio, Sergio and Mazzucchi, S.},
2709 booktitle = {Seminar on Stochastic Analysis, Random Fields and Applications VI},
2710 file = {::},
2711 number = {332},
2712 pages = {3--21},
2713 publisher = {Springer},
2714 title = {{The trace formula for the heat semigroup with polynomial potential}},
2715 url = {http://www.springerlink.com/index/X6654U4VL3G450K9.pdf},
2716 year = {2011}
2717 }
2718 @article{Fitzsimmons1988,
2719 author = {Fitzsimmons, P. J. and Getoor, R. K.},
2720 file = {::},
2721 journal = {Mathematische Annalen},
2722 number = {3},
2723 pages = {495--512},
2724 publisher = {Springer},
2725 title = {{On the potential theory of symmetric Markov processes}},
2726 url = {http://www.springerlink.com/index/V5836436X0352T13.pdf},
2727 volume = {281},
2728 year = {1988}
2729 }
2730 @article{millet.morien05,
2731 author = {Millet, Annie and Morien, Pierre-Luc},
2732 doi = {10.1016/j.spa.2005.02.004},
2733 file = {::},
2734 issn = {03044149},
2735 journal = {Stochastic Processes and their Applications},
2736 keywords = {gaussian noise,green function,implicit and explicit space,laboratoire de probabilite,numerical simulations,parabolic spde,space correlation,speed of convergence,time discretization schemes,\~{a} corresponding author},
2737 month = jul,
2738 number = {7},
2739 pages = {1073--1106},
2740 title = {{On implicit and explicit discretization schemes for parabolic SPDEs in any dimension}},
2741 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414905000189},
2742 volume = {115},
2743 year = {2005}
2744 }
2745 @article{Sturm2003,
2746 author = {Sturm, A},
2747 file = {::},
2748 journal = {Electronic Journal of Probability},
2749 keywords = {2000,2002,2003,60f05,60j80,60k35,ams subject classification,april 11,colored noise,existence theorem,final version accepted on,heat equation,particle representation,primary 60h15,random environment,secondary 60k37,september 17,stochastic partial differential equation,submitted to ejp on,superprocess,weak convergence},
2750 number = {2000},
2751 pages = {1--39},
2752 title = {{On convergence of population processes in random environments to the stochastic heat equation with colored noise}},
2753 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/include/getdoc9eac.pdf?id=2912&article=1347&mode=pdf},
2754 year = {2003}
2755 }
2756 @article{Cox2011,
2757 archivePrefix = {arXiv},
2758 arxivId = {arXiv:1103.1676v1},
2759 author = {Cox, J.T. and Durrett, Richard and Perkins, E.},
2760 eprint = {arXiv:1103.1676v1},
2761 file = {::},
2762 journal = {Arxiv preprint arXiv:1103.1676},
2763 keywords = {and phrases,evo-,interacting particle systems,lotka-volterra model,lutionary game theory,reaction diffusion equation,voter model},
2764 pages = {1--106},
2765 title = {{Voter model perturbations and reaction diffusion equations}},
2766 url = {http://arxiv.org/abs/1103.1676},
2767 year = {2011}
2768 }
2769 @article{chenal.millet97,
2770 author = {Chenal, F. and Millet, A.},
2771 journal = {Stochastic Process. Appl.},
2772 number = {2},
2773 pages = {161----186},
2774 title = {{Uniform large deviations for parabolic {SPDE}s and applications}},
2775 volume = {72},
2776 year = {1997}
2777 }
2778 @article{holling73,
2779 author = {Holling, C.S.},
2780 file = {::},
2781 journal = {Annual review of ecology and systematics},
2782 pages = {1--23},
2783 publisher = {JSTOR},
2784 title = {{Resilience and stability of ecological systems}},
2785 url = {http://www.jstor.org/stable/10.2307/2096802},
2786 volume = {4},
2787 year = {1973}
2788 }
2789 @article{Chung1973,
2790 author = {Chung, K.L.},
2791 file = {::},
2792 journal = {Ann. Inst. Fourier (Grenoble)},
2793 pages = {313--322},
2794 title = {{Probabilistic approach in potential theory to the equilibrium problem}},
2795 url = {http://archive.numdam.org/article/AIF_1973__23_3_313_0.pdf},
2796 volume = {23},
2797 year = {1973}
2798 }
2799 @article{Funaki2004d,
2800 author = {Funaki, Tadahisa},
2801 doi = {10.1214/009117904000000199},
2802 file = {::;::},
2803 issn = {0091-1798},
2804 journal = {The Annals of Probability},
2805 month = apr,
2806 number = {2},
2807 pages = {1228--1246},
2808 title = {{Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension}},
2809 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884850/ http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884849/},
2810 volume = {32},
2811 year = {2004}
2812 }
2813 @article{Garcia-Pelayo1997,
2814 author = {Garc\'{\i}a-Pelayo, Ricardo and Stadler, Peter F.},
2815 doi = {10.1016/S0167-2789(97)00091-2},
2816 file = {::},
2817 issn = {01672789},
2818 journal = {Physica D: Nonlinear Phenomena},
2819 keywords = {graph laplacian,isotropy,meta-stable states,rugged landscapes,xy-hamiltonian},
2820 month = sep,
2821 number = {2-4},
2822 pages = {240--254},
2823 title = {{Correlation length, isotropy and meta-stable states}},
2824 url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278997000912},
2825 volume = {107},
2826 year = {1997}
2827 }
2828 @article{Dimock1974,
2829 author = {Dimock, Jonathan and Glimm, James},
2830 file = {::},
2831 journal = {Advances in Mathematics},
2832 pages = {58--83},
2833 title = {{Mesures on schwartz distribution space and applications to $P(\phi)_2$ field theories}},
2834 volume = {12},
2835 year = {1974}
2836 }
2837 @article{Bellettini2005,
2838 author = {Bellettini, G. and {De Masi}, a. and Presutti, E.},
2839 doi = {10.1063/1.1990107},
2840 file = {::},
2841 issn = {00222488},
2842 journal = {Journal of Mathematical Physics},
2843 number = {8},
2844 pages = {083302},
2845 title = {{Energy levels of a nonlocal functional}},
2846 url = {http://link.aip.org/link/JMAPAQ/v46/i8/p083302/s1&Agg=doi},
2847 volume = {46},
2848 year = {2005}
2849 }
2850 @article{Billingsley1974,
2851 author = {Billingsley, P.},
2852 file = {::},
2853 journal = {The Annals of Probability},
2854 number = {5},
2855 pages = {749--791},
2856 publisher = {JSTOR},
2857 title = {{The probability theory of additive arithmetic functions}},
2858 url = {http://www.jstor.org/stable/10.2307/2959305},
2859 volume = {2},
2860 year = {1974}
2861 }
2862 @misc{Mattingly2007,
2863 author = {Mattingly, Jonathan C.},
2864 booktitle = {Saint-Flour lecture notes},
2865 file = {::},
2866 title = {{Ergodicity of dissipative spdes}},
2867 url = {http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:Ergodicity+of+Dissipative+SPDEs#0},
2868 year = {2007}
2869 }
2870 @article{Hairer2009c,
2871 author = {Hairer, Martin},
2872 file = {::},
2873 journal = {Arxiv preprint arXiv:0910.0315},
2874 number = {1},
2875 pages = {1--6},
2876 title = {{Hypoellipticity in infinite dimensions}},
2877 url = {http://arxiv.org/abs/0910.0315},
2878 year = {2009}
2879 }
2880 @article{Simon1977,
2881 author = {Simon, Barry},
2882 file = {::},
2883 journal = {Advances in Mathematics},
2884 number = {3},
2885 pages = {244--273},
2886 publisher = {Elsevier},
2887 title = {{Notes on infinite determinants of Hilbert space operators}},
2888 url = {http://www.sciencedirect.com/science/article/pii/0001870877900573},
2889 volume = {24},
2890 year = {1977}
2891 }
2892 @misc{Hur2008,
2893 archivePrefix = {arXiv},
2894 arxivId = {arXiv:0805.0079v1},
2895 author = {Hur, Jin and Min, Hyunsoo},
2896 eprint = {arXiv:0805.0079v1},
2897 file = {::},
2898 pages = {1--28},
2899 title = {{A Fast Way to Compute Functional Determinants of Radially Symmetric Partial Differential Operators in General Dimensions}},
2900 year = {2008}
2901 }
2902 @article{Getoor1973a,
2903 author = {Getoor, RK and Sharpe, MJ},
2904 file = {::},
2905 journal = {The Annals of Probability},
2906 number = {4},
2907 pages = {550--569},
2908 publisher = {Institute of Mathematical Statistics},
2909 title = {{Last exit times and additive functionals}},
2910 url = {http://projecteuclid.org/euclid.aop/1176996885},
2911 volume = {1},
2912 year = {1973}
2913 }
2914 @article{Cassandro1995,
2915 author = {Cassandro, Marzio and Marra, R. and Presutti, E.},
2916 file = {::},
2917 journal = {Journal of statistical physics},
2918 keywords = {2,an extended version of,critical uctuations,euclidean eld theory,in a d,in this short communication,is,ising model,ising model with kac,kac potential,potentials,proofs will follow in,recall,that the kac hamiltonian,this note,to the critical temperature,we study the corrections},
2919 number = {3},
2920 pages = {1131--1138},
2921 publisher = {Springer},
2922 title = {{Corrections to the critical temperature in 2d Ising systems with Kac potentials}},
2923 url = {http://www.springerlink.com/index/7084R2NH31076G94.pdf},
2924 volume = {78},
2925 year = {1995}
2926 }
2927 @article{Scheffer2003,
2928 author = {Scheffer, Marten and Carpenter, Stephen R.},
2929 doi = {10.1016/j.tree.2003.09.002},
2930 file = {::},
2931 issn = {01695347},
2932 journal = {Trends in Ecology \& Evolution},
2933 month = dec,
2934 number = {12},
2935 pages = {648--656},
2936 title = {{Catastrophic regime shifts in ecosystems: linking theory to observation}},
2937 url = {http://linkinghub.elsevier.com/retrieve/pii/S0169534703002787},
2938 volume = {18},
2939 year = {2003}
2940 }
2941 @article{Mehlig1992,
2942 author = {Mehlig, Bernhard and Forrest, Bruce M.},
2943 file = {::},
2944 journal = {Zeitschrift f\"{u}r Physik B},
2945 pages = {89--96},
2946 title = {{Universality in the critical two-dimensional $\phi^4$ model}},
2947 volume = {89},
2948 year = {1992}
2949 }
2950 @article{Duan2009,
2951 author = {Duan, Jinqiao and Millet, Annie},
2952 doi = {10.1016/j.spa.2008.10.004},
2953 file = {::},
2954 issn = {03044149},
2955 journal = {Stochastic Processes and their Applications},
2956 keywords = {b,boussinesq equations,enard convection,equations,impact of noise on,large deviations,multiplicative noise,stochastic navier,stochastic pdes,stokes,system evolution},
2957 month = jun,
2958 number = {6},
2959 pages = {2052--2081},
2960 publisher = {Elsevier},
2961 title = {{Large deviations for the Boussinesq equations under random influences}},
2962 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908001579},
2963 volume = {119},
2964 year = {2009}
2965 }
2966 @article{kirsten.mckane04,
2967 author = {Kirsten, Klaus and McKane, Alan J.},
2968 doi = {10.1088/0305-4470/37/16/014},
2969 file = {::},
2970 issn = {0305-4470},
2971 journal = {Journal of Physics A: Mathematical and General},
2972 month = apr,
2973 pages = {4649--4670},
2974 title = {{Functional determinants for general Sturm–Liouville problems}},
2975 url = {http://stacks.iop.org/0305-4470/37/i=16/a=014?key=crossref.7848aae42b4fc923ee79d511cf1cab33},
2976 volume = {37},
2977 year = {2004}
2978 }
2979 @article{brunovsky.chow84,
2980 author = {Brunovsky, P. and Chow, S.N.},
2981 file = {::},
2982 journal = {Journal of differential equations},
2983 number = {1},
2984 pages = {1--23},
2985 publisher = {Academic Press},
2986 title = {{Generic properties of stationary state solutions of reaction-diffusion equations}},
2987 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=9669009},
2988 volume = {53},
2989 year = {1984}
2990 }
2991 @phdthesis{Gentil2001,
2992 author = {Gentil, Ivan},
2993 file = {::},
2994 pages = {147},
2995 title = {{In\'{e}galit\'{e}s de Sobolev logarithmiques et hypercontractivit\'{e} en m\'{e}canique statistique et en EDP}},
2996 year = {2001}
2997 }
2998 @article{Bansaye2011,
2999 author = {Bansaye, Vincent and Lambert, Amaury},
3000 file = {::},
3001 number = {December},
3002 title = {{Past, growth and persistence of source-sink metapopulations}},
3003 url = {http://hal.archives-ouvertes.fr/hal-00639011/},
3004 year = {2011}
3005 }
3006 @article{Andrew2003,
3007 author = {Andrew, A.L.},
3008 file = {::},
3009 journal = {BIT Numerical Mathematics},
3010 keywords = {asymptotic correction,computation of higher eigenvalues,liouville problems,method,numerov,s,sturm},
3011 number = {3},
3012 pages = {485--503},
3013 publisher = {Springer},
3014 title = {{Asymptotic correction of more Sturm–Liouville eigenvalue estimates}},
3015 url = {http://www.springerlink.com/index/V68M787714507737.pdf},
3016 volume = {43},
3017 year = {2003}
3018 }
3019 @article{Blomker2004,
3020 author = {Bl\"{o}mker, D. and Hairer, Martin},
3021 file = {::},
3022 journal = {Communications in mathematical physics},
3023 number = {3},
3024 pages = {515--555},
3025 publisher = {Springer},
3026 title = {{Multiscale expansion of invariant measures for SPDEs}},
3027 url = {http://www.springerlink.com/index/HB88RP1WP5NNJTKP.pdf},
3028 volume = {251},
3029 year = {2004}
3030 }
3031 @article{faris.jonalasinio82,
3032 author = {Faris, William G. and Jona-Lasinio, G.},
3033 journal = {J. Phys. A},
3034 number = {10},
3035 pages = {3025----3055},
3036 title = {{Large fluctuations for a nonlinear heat equation with noise}},
3037 volume = {15},
3038 year = {1982}
3039 }
3040 @article{Cattiaux2010c,
3041 abstract = {We are interested in the long time behavior of a two-type density-dependent biological population conditioned on non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic Lotka-Volterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not to blow up. We study the existence and uniqueness of a quasi-stationary distribution, that is convergence to equilibrium conditioned on non-extinction. To this aim we generalize in two-dimensions spectral tools developed for one-dimensional generalized Feller diffusion processes. The existence proof of a quasi-stationary distribution is reduced to the one for a d-dimensional Kolmogorov diffusion process under a symmetry assumption. The symmetry we need is satisfied under a local balance condition relying the ecological rates. A novelty is the outlined relation between the uniqueness of the quasi-stationary distribution and the ultracontractivity of the killed semi-group. By a comparison between the killing rates for the populations of each type and the one of the global population, we show that the quasi-stationary distribution can be either supported by individuals of one (the strongest one) type or supported by individuals of the two types. We thus highlight two different long time behaviors depending on the parameters of the model: either the model exhibits an intermediary time scale for which only one type (the dominant trait) is surviving, or there is a positive probability to have coexistence of the two species.},
3042 author = {Cattiaux, Patrick and M\'{e}l\'{e}ard, Sylvie},
3043 doi = {10.1007/s00285-009-0285-4},
3044 file = {::},
3045 issn = {1432-1416},
3046 journal = {Journal of mathematical biology},
3047 keywords = {Animals,Behavior, Animal,Biostatistics,Computer Simulation,Computer Simulation: statistics & numerical data,Extinction, Biological,Models, Statistical,Population Dynamics,Stochastic Processes},
3048 month = jun,
3049 number = {6},
3050 pages = {797--829},
3051 pmid = {19649634},
3052 title = {{Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction.}},
3053 url = {http://www.ncbi.nlm.nih.gov/pubmed/19649634},
3054 volume = {60},
3055 year = {2010}
3056 }
3057 @article{Berglund2001b,
3058 archivePrefix = {arXiv},
3059 arxivId = {arXiv:math/0111178v1},
3060 author = {Berglund, Nils},
3061 eprint = {0111178v1},
3062 file = {::},
3063 journal = {Arxiv preprint math/0111178},
3064 primaryClass = {arXiv:math},
3065 title = {{Perturbation theory of dynamical systems}},
3066 url = {http://arxiv.org/abs/math/0111178},
3067 year = {2001}
3068 }
3069 @book{stroock.varadhan79,
3070 author = {Stroock, Daniel W. and Varadhan, S. R. Srinivasa},
3071 pages = {xii+338},
3072 publisher = {Springer-Verlag},
3073 title = {{Multidimensional diffusion processes}},
3074 url = {http://books.google.com/books?hl=en&lr=&id=DuDsmoyqCy4C&oi=fnd&pg=PR11&dq=Multidimensional+diffusion+processes&ots=tUecDBwkyB&sig=DXYS2kJqgHPy6nUA4kGXlIN1Q7o},
3075 year = {1979}
3076 }
3077 @article{Egorov1992,
3078 author = {Egorov, Yuri E.},
3079 file = {::},
3080 journal = {S\'{e}minaire EDP (Polytechnique)},
3081 pages = {1--11},
3082 title = {{Sur des estimations des valeurs propres d'op\'{e}rateurs elliptiques}},
3083 volume = {16},
3084 year = {1992}
3085 }
3086 @article{Rougemont2002a,
3087 author = {Rougemont, Jacques},
3088 file = {::},
3089 pages = {423--448},
3090 title = {{Space-Time Invariant Measures , Entropy , and Dimension for Stochastic Ginzburg – Landau Equations}},
3091 volume = {448},
3092 year = {2002}
3093 }
3094 @article{ColindeVerdiere1999c,
3095 author = {{Colin de Verdi\`{e}re}, Yves},
3096 file = {::;::;::},
3097 journal = {Annales de l'institut Fourier},
3098 number = {3},
3099 pages = {861--881},
3100 title = {{D\'{e}terminants et int\'{e}grales de Fresnel}},
3101 volume = {49},
3102 year = {1999}
3103 }
3104 @article{ColindeVerdiere1999b,
3105 author = {{Colin de Verdi\`{e}re}, Yves},
3106 file = {::},
3107 journal = {Annales de l'institut Fourier},
3108 number = {3},
3109 pages = {861--881},
3110 title = {{D\'{e}terminants et int\'{e}grales de Fresnel}},
3111 volume = {49},
3112 year = {1999}
3113 }
3114 @article{Bak1997,
3115 author = {Bak, P. and Boettcher, Stefan},
3116 file = {::},
3117 journal = {Physica D: Nonlinear Phenomena},
3118 keywords = {avalanches,glassy dynamics,landscapes,punctuated equilibrium,self-organized criticality},
3119 number = {2-4},
3120 pages = {143--150},
3121 publisher = {Elsevier},
3122 title = {{Self-organized criticality and punctuated equilibria}},
3123 url = {http://www.sciencedirect.com/science/article/pii/S016727899700078X},
3124 volume = {107},
3125 year = {1997}
3126 }
3127 @article{ColindeVerdiere1999,
3128 author = {{Colin de Verdi\`{e}re}, Yves},
3129 file = {::},
3130 journal = {Annales de l'institut Fourier},
3131 number = {3},
3132 pages = {861--881},
3133 title = {{D\'{e}terminants de int\'{e}grales de Fresnel}},
3134 volume = {49},
3135 year = {1999}
3136 }
3137 @article{Burghelea1991,
3138 author = {Burghelea, D. and Friedlander, L. and Kappeler, T.},
3139 file = {::},
3140 journal = {Communications in Mathematical Physics},
3141 number = {1},
3142 pages = {1--18},
3143 publisher = {Springer},
3144 title = {{On the determination of elliptic differential and finite difference operators in vector bundles overS 1}},
3145 url = {http://www.springerlink.com/index/k46538n72j561608.pdf},
3146 volume = {138},
3147 year = {1991}
3148 }
3149 @article{gyongy.pardoux93,
3150 author = {Gy\"{o}ngy, Istv\'{a}n and Pardoux, Etienne},
3151 file = {::},
3152 journal = {Probability theory and related fields},
3153 pages = {413--425},
3154 title = {{On quasi-linear stochastic partial differential equations}},
3155 url = {http://www.springerlink.com/index/J38830Q5W0615863.pdf},
3156 volume = {94},
3157 year = {1993}
3158 }
3159 @article{BBI09,
3160 archivePrefix = {arXiv},
3161 arxivId = {arXiv:0806.4478v1},
3162 author = {Bianchi, Alessandra and Bovier, Anton and Ioffe, Dmitry},
3163 eprint = {arXiv:0806.4478v1},
3164 file = {::},
3165 journal = {Electronic Journal of Probability},
3166 keywords = {and phrases,and the weierstrass-institute for,applied analysis and stochastics,capacity,dirichlet form,disordered system,gif,glauber dynamics,haifa,hospitality of the technion,metastability,potential theory,random field curie-weiss model,the german-israeli foundation,the kind,this research was supported,through a grant by},
3167 pages = {1541--1603},
3168 publisher = {WIAS},
3169 title = {{Sharp asymptotics for metastability in the random field Curie-Weiss model}},
3170 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/include/getdoc8e1c.pdf?id=5163&article=1984&mode=pdf},
3171 volume = {14},
3172 year = {2009}
3173 }
3174 @article{BFG07a,
3175 archivePrefix = {arXiv},
3176 arxivId = {arXiv:math/0611647v2},
3177 author = {Berglund, Nils and Fernandez, Bastien and Gentz, Barbara},
3178 eprint = {0611647v2},
3179 file = {::},
3180 journal = {Nonlinearity},
3181 keywords = {and phrases,diffusive coupling,interacting diffusions,large deviations,lattice dynamical systems,metastability,most probable transition,open systems,paths,spatially extended systems,stochastic differential equations,synchronisation,transitions times,wentzell-freidlin theory},
3182 pages = {2551},
3183 primaryClass = {arXiv:math},
3184 publisher = {IOP Publishing},
3185 title = {{Metastability in interacting nonlinear stochastic differential equations: I. From weak coupling to synchronization}},
3186 url = {http://iopscience.iop.org/0951-7715/20/11/006},
3187 volume = {20},
3188 year = {2007}
3189 }
3190 @article{helffer.nier06,
3191 author = {Helffer, Bernard and Nier, Francis},
3192 journal = {{M\'em. Soc. Math. Fr. (N.S.)}},
3193 pages = {vi+89},
3194 title = {{Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary}},
3195 url = {http://smf.emath.fr/Publications/Memoires/2006/105/pdf/smf_mem-ns_105.pdf},
3196 volume = {105},
3197 year = {2006}
3198 }
3199 @article{Dunne2006,
3200 archivePrefix = {arXiv},
3201 arxivId = {arXiv:hep-th/0607066v1},
3202 author = {Dunne, G.V. and Kirsten, Klaus},
3203 eprint = {0607066v1},
3204 file = {::},
3205 journal = {Journal of Physics A: Mathematical and General},
3206 pages = {11915},
3207 primaryClass = {arXiv:hep-th},
3208 publisher = {IOP Publishing},
3209 title = {{Functional determinants for radial operators}},
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4841 number = {1},
4842 pages = {207--241},
4843 title = {{Geometry of heteroclinic cascades in scalar parabolic differential equations}},
4844 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039601941142 http://www.springerlink.com/index/X00M5X50564071M7.pdf},
4845 volume = {14},
4846 year = {2002}
4847 }
4848 @article{Funaki1991,
4849 author = {Funaki, Tadahisa},
4850 file = {::},
4851 journal = {Osaka J. Math},
4852 pages = {463--494},
4853 title = {{The reversible measures of multi-dimensional Ginzburg-Landau type continuum model}},
4854 url = {http://ir.library.osaka-u.ac.jp/metadb/up/LIBOJMK01/ojm28_03_01.pdf},
4855 volume = {28},
4856 year = {1991}
4857 }
4858 @article{Getoor1973b,
4859 author = {Getoor, R. K. and Sharpe, M. J.},
4860 file = {::},
4861 journal = {Indiana University Mathematics Journal},
4862 number = {5},
4863 pages = {377--404},
4864 title = {{Last exit decompositions and distributions}},
4865 url = {http://d.wanfangdata.com.cn/NSTLQK_10.1512-iumj.1973.23.23031.aspx},
4866 volume = {23},
4867 year = {1973}
4868 }
4869 @book{Herrmann2006,
4870 author = {Herrmann, Samuel and Imkeller, Peter and Peithmann, Dierk},
4871 booktitle = {The Annals of Applied Probability},
4872 doi = {10.1214/105051606000000385},
4873 file = {::},
4874 isbn = {1050516060},
4875 issn = {1050-5164},
4876 month = nov,
4877 number = {4},
4878 pages = {1851--1892},
4879 title = {{Transition times and stochastic resonance for multidimensional diffusions with time periodic drift: A large deviations approach}},
4880 url = {http://projecteuclid.org/getRecord?id=euclid.aoap/1169065210},
4881 volume = {16},
4882 year = {2006}
4883 }
4884 @article{Nagase2011,
4885 author = {Nagase, Yuko},
4886 doi = {10.1007/s00229-011-0458-5},
4887 file = {::},
4888 issn = {0025-2611},
4889 journal = {Manuscripta Mathematica},
4890 month = apr,
4891 number = {1-2},
4892 pages = {81--106},
4893 title = {{Action minimization for an Allen-Cahn equation with an unequal double-well potential}},
4894 url = {http://www.springerlink.com/index/10.1007/s00229-011-0458-5},
4895 volume = {137},
4896 year = {2011}
4897 }
4898 @article{Jentzen2009a,
4899 author = {Jentzen, Arnulf},
4900 doi = {10.1007/s11118-009-9139-3},
4901 file = {::},
4902 issn = {0926-2601},
4903 journal = {Potential Analysis},
4904 keywords = {2000,35k90,60h15,65c30,equation,global lipschitz,higher order approximation,mathematics subject classifications,parabolic stochastic partial differential,pathwise approximation,strong error criteria},
4905 month = jul,
4906 number = {4},
4907 pages = {375--404},
4908 title = {{Pathwise Numerical Approximations of SPDEs with Additive Noise under Non-global Lipschitz Coefficients}},
4909 url = {http://www.springerlink.com/index/10.1007/s11118-009-9139-3},
4910 volume = {31},
4911 year = {2009}
4912 }
4913 @article{Albers2001b,
4914 author = {Albers, W.},
4915 doi = {10.1214/074921706000000239},
4916 file = {::;::},
4917 isbn = {0749217060000},
4918 journal = {Lecture Notes-Monograph Series},
4919 keywords = {-statistics,and,and phrases,berry-esseen,bootstrap,empirical,expansion,l-,r-,second order asymptotics,symmetric statistics},
4920 number = {2006},
4921 pages = {2--20},
4922 publisher = {JSTOR},
4923 title = {{From A to Z: Asymptotic expansions by van Zwet}},
4924 url = {http://www.jstor.org/stable/10.2307/4356103},
4925 volume = {36},
4926 year = {2001}
4927 }
4928 @article{Scott1999,
4929 author = {Scott, Simon and Wojciechowski, Krzysztof},
4930 file = {::},
4931 journal = {Comptes Rendus de l'Acad\'{e}mie des Sciences-Series I-Mathematics},
4932 number = {2},
4933 pages = {139--144},
4934 publisher = {Elsevier},
4935 title = {{$\zeta$-determinant and the Quillen determinant on the Grassmannian of elliptic self-adjoint boundary conditions}},
4936 url = {http://www.sciencedirect.com/science/article/pii/S0764444299801529},
4937 volume = {328},
4938 year = {1999}
4939 }
4940 @article{Assaf2011,
4941 archivePrefix = {arXiv},
4942 arxivId = {arXiv:1011.0322v1},
4943 author = {Assaf, Michael and Mobilia, Mauro},
4944 eprint = {arXiv:1011.0322v1},
4945 file = {::},
4946 journal = {Journal of Theoretical Biology},
4947 number = {0},
4948 pages = {1--27},
4949 publisher = {Elsevier},
4950 title = {{Fixation of a deleterious allele under mutation pressure and finite selection intensity}},
4951 url = {http://www.sciencedirect.com/science/article/pii/S0022519311000373},
4952 year = {2011}
4953 }
4954 @article{Steiner2011,
4955 archivePrefix = {arXiv},
4956 arxivId = {arXiv:1106.3573v1},
4957 author = {Steiner, J and Wieczoreck, H},
4958 eprint = {arXiv:1106.3573v1},
4959 file = {::},
4960 journal = {Arxiv preprint arXiv:},
4961 number = {1},
4962 pages = {1--26},
4963 title = {{The Formation and Coarsening of the Concertina Pattern}},
4964 url = {http://arxiv.org/abs/1106.3573},
4965 year = {2011}
4966 }
4967 @article{Meerson2011,
4968 archivePrefix = {arXiv},
4969 arxivId = {arXiv:1008.4854v1},
4970 author = {Meerson, Baruch and Sasorov, P.V.},
4971 eprint = {arXiv:1008.4854v1},
4972 file = {::},
4973 journal = {Physical Review E},
4974 number = {1},
4975 pages = {011129},
4976 publisher = {APS},
4977 title = {{Extinction rates of established spatial populations}},
4978 url = {http://pre.aps.org/abstract/PRE/v83/i1/e011129},
4979 volume = {83},
4980 year = {2011}
4981 }
4982 @article{Fiedler2009,
4983 author = {Fiedler, Bernold and Rocha, Carlos},
4984 doi = {10.1515/CRELLE.2009.076},
4985 file = {::},
4986 issn = {0075-4102},
4987 journal = {Journal f\"{u}r die reine und angewandte Mathematik (Crelles Journal)},
4988 month = oct,
4989 number = {635},
4990 pages = {71--96},
4991 title = {{Connectivity and design of planar global attractors of Sturm type, I: Bipolar orientations and Hamiltonian paths}},
4992 url = {http://www.reference-global.com/doi/abs/10.1515/CRELLE.2009.076},
4993 volume = {2009},
4994 year = {2009}
4995 }
4996 @article{Gibbs2002,
4997 author = {Gibbs, A.L. and Su, F.E.},
4998 file = {::},
4999 journal = {International statistical review},
5000 number = {3},
5001 pages = {419--435},
5002 publisher = {Wiley Online Library},
5003 title = {{On choosing and bounding probability metrics}},
5004 url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1751-5823.2002.tb00178.x/abstract},
5005 volume = {70},
5006 year = {2002}
5007 }
5008 @article{Bertini2008,
5009 author = {Bertini, Lorenzo and Brassesco, Stella and Butt\`{a}, Paolo},
5010 file = {::},
5011 journal = {Archive for Rational Mechanics and Analysis},
5012 number = {3},
5013 pages = {477--516},
5014 publisher = {Springer},
5015 title = {{Dobrushin States in the $\phi_1^4$ Model}},
5016 url = {http://www.springerlink.com/index/7111352011336765.pdf},
5017 volume = {190},
5018 year = {2008}
5019 }
5020 @book{dellacherie.meyer87,
5021 address = {Paris},
5022 author = {Dellacherie, Claude and Meyer, Paul-Andr\'{e}},
5023 pages = {xii+378},
5024 publisher = {Hermann},
5025 title = {{Probabilit\'es et potentiel. {C}ha\-pitres {XII}--{XVI}.}},
5026 year = {1987}
5027 }
5028 @article{Voter1998,
5029 author = {Voter, Arthur},
5030 doi = {10.1103/PhysRevB.57.R13985},
5031 file = {::},
5032 issn = {0163-1829},
5033 journal = {Physical Review B},
5034 month = jun,
5035 number = {22},
5036 pages = {R13985--R13988},
5037 title = {{Parallel replica method for dynamics of infrequent events}},
5038 url = {http://link.aps.org/doi/10.1103/PhysRevB.57.R13985},
5039 volume = {57},
5040 year = {1998}
5041 }
5042 @article{Huillet2011,
5043 author = {Huillet, Thierry},
5044 doi = {10.1088/1742-5468/2011/02/P02016},
5045 file = {::},
5046 issn = {1742-5468},
5047 journal = {Journal of Statistical Mechanics: Theory and Experiment},
5048 month = feb,
5049 number = {02},
5050 pages = {P02016},
5051 title = {{On the Karlin–Kimura approaches to the Wright–Fisher diffusion with fluctuating selection}},
5052 url = {http://stacks.iop.org/1742-5468/2011/i=02/a=P02016?key=crossref.766bf36c47ddb77abbb765bb97545de0},
5053 volume = {2011},
5054 year = {2011}
5055 }
5056 @article{Rey-Bellet2002,
5057 author = {Rey-Bellet, Luc and Thomas, Lawrence E.},
5058 file = {::},
5059 journal = {Communications in mathematical physics},
5060 pages = {305--329},
5061 title = {{Exponential convergence to non-equilibrium stationary states in classical statistical mechanics}},
5062 url = {http://www.springerlink.com/index/qajgj1ejgp1j3ccr.pdf},
5063 volume = {225},
5064 year = {2002}
5065 }
5066 @article{Erbar2010,
5067 archivePrefix = {arXiv},
5068 arxivId = {arXiv:1012.2718v1},
5069 author = {Erbar, Matthias},
5070 eprint = {arXiv:1012.2718v1},
5071 file = {::},
5072 journal = {Arxiv preprint arXiv:1012.2718},
5073 keywords = {invariant measure,large deviations,stochastic reaction-diffusion equation},
5074 number = {1},
5075 pages = {1--14},
5076 title = {{Low noise limit for the invariant measure of a multi-dimensional stochastic Allen-Cahn equation}},
5077 url = {http://arxiv.org/abs/1012.2718},
5078 year = {2010}
5079 }
5080 @article{Fix1967c,
5081 author = {Fix, George},
5082 file = {::;::},
5083 journal = {Journal of Mathematical Analysis and Applications},
5084 pages = {519--525},
5085 title = {{Asymptotic Eigenvalues of Sturm-Liouville Systems}},
5086 volume = {19},
5087 year = {1967}
5088 }
5089 @article{FRW04,
5090 author = {Fiedler, Bernold and Rocha, Carlos and Wolfrum, Matthias},
5091 doi = {10.1016/j.jde.2003.10.027},
5092 file = {::},
5093 issn = {00220396},
5094 journal = {Journal of Differential Equations},
5095 keywords = {global attractor,heteroclinic orbit,zero number},
5096 month = jun,
5097 number = {1},
5098 pages = {99--138},
5099 title = {{Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle}},
5100 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039604000683},
5101 volume = {201},
5102 year = {2004}
5103 }
5104 @article{Berglund2002,
5105 archivePrefix = {arXiv},
5106 arxivId = {arXiv:cond-mat/0110180v1},
5107 author = {Berglund, Nils and Gentz, Barbara},
5108 eprint = {0110180v1},
5109 file = {::},
5110 journal = {Journal of Physics A: Mathematical and General},
5111 keywords = {and phrases,bifurcation delay,double-well potential,dynamical hysteresis,exit time,first-,fokker,langevin equation,planck equation,scaling laws,stochastic resonance,white noise},
5112 pages = {2057},
5113 primaryClass = {arXiv:cond-mat},
5114 publisher = {IOP Publishing},
5115 title = {{Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems}},
5116 url = {http://iopscience.iop.org/0305-4470/35/9/301},
5117 volume = {35},
5118 year = {2002}
5119 }
5120 @inproceedings{levit.smilansky77,
5121 author = {Levit, S. and Smilansky, U.},
5122 booktitle = {Proc. Amer. Math. Soc},
5123 file = {::},
5124 number = {2},
5125 pages = {299--302},
5126 title = {{A theorem on infinite products of eigenvalues of Sturm–Liouville type operators}},
5127 url = {http://www.ams.org/journals/proc/1977-065-02/S0002-9939-1977-0457836-8/S0002-9939-1977-0457836-8.pdf},
5128 volume = {65},
5129 year = {1977}
5130 }
5131 @article{Majda1999,
5132 abstract = {There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction. Here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory. This analysis demonstrates the potential need for more sophisticated models beyond stable linear Langevin equations. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. The strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta-plane with topography and a mean flow. In this example, the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom.},
5133 author = {Majda, Andrew J. and Timofeyev, Ilya and Vanden-Eijnden, Eric},
5134 file = {::},
5135 issn = {0027-8424},
5136 journal = {Proceedings of the National Academy of Sciences of the United States of America},
5137 month = dec,
5138 number = {26},
5139 pages = {14687--91},
5140 pmid = {10611273},
5141 title = {{Models for stochastic climate prediction.}},
5142 url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=24708&tool=pmcentrez&rendertype=abstract},
5143 volume = {96},
5144 year = {1999}
5145 }
5146 @article{angenent86,
5147 author = {Angenent, Sigurd B.},
5148 file = {::},
5149 journal = {Journal of differential equations},
5150 pages = {427--442},
5151 title = {{The Morse-Smale property for a semi-linear parabolic equation}},
5152 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=8771440},
5153 volume = {62},
5154 year = {1986}
5155 }
5156 @article{Matkowsky1977,
5157 author = {Matkowsky, B.J. and Schuss, Z.},
5158 file = {::},
5159 journal = {SIAM Journal on Applied Mathematics},
5160 number = {2},
5161 pages = {365--382},
5162 publisher = {JSTOR},
5163 title = {{The exit problem for randomly perturbed dynamical systems}},
5164 url = {http://www.jstor.org/stable/10.2307/2100884},
5165 volume = {33},
5166 year = {1977}
5167 }
5168 @article{Albeverio2009,
5169 author = {Albeverio, Sergio and Mandrekar, V. and R\"{u}diger, B.},
5170 doi = {10.1016/j.spa.2008.03.006},
5171 file = {::},
5172 issn = {03044149},
5173 journal = {Stochastic Processes and their Applications},
5174 keywords = {additive,compensated poisson random measures,contraction semigroups,corresponding author,differential equations,hilbert spaces,martingale measures,mild solutions of stochastic,processes,pseudo-differential operators,random hilbert valued functions,stochastic integrals on separable},
5175 month = mar,
5176 number = {3},
5177 pages = {835--863},
5178 title = {{Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian L\'{e}vy noise}},
5179 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908000604},
5180 volume = {119},
5181 year = {2009}
5182 }
5183 @article{\'Alvarez2000,
5184 archivePrefix = {arXiv},
5185 arxivId = {arXiv:cond-mat/9905034v1},
5186 author = {{\'A}lvarez, Luis Fern{\'a}ndez and Pla, Oscar and Chubykalo, Oskana},
5187 eprint = {9905034v1},
5188 file = {::},
5189 journal = {Physical Review B},
5190 pages = {1--4},
5191 primaryClass = {arXiv:cond-mat},
5192 title = {{Quasiperiodicity, bistability, and chaos in the Landau-Lifshitz equation}},
5193 url = {http://prb.aps.org/abstract/PRB/v61/i17/p11613_1},
5194 year = {2000}
5195 }
5196 @article{Berkov2005,
5197 author = {Berkov, D.V. and Gorn, N.L.},
5198 file = {::},
5199 journal = {Journal of magnetism and magnetic materials},
5200 keywords = {-b,1,25,30,40,72,75,colored noise,decades both micromagnetic simula-,ds,during the last two,gb,introduction and motivation,mg,micromagnetic simulations,pacs,spin injection,stochastic dynamics},
5201 number = {1},
5202 pages = {442--448},
5203 publisher = {Elsevier},
5204 title = {{Stochastic dynamic simulations of fast remagnetization processes: recent advances and applications}},
5205 url = {http://www.sciencedirect.com/science/article/pii/S0304885304018323},
5206 volume = {290},
5207 year = {2005}
5208 }
5209 @article{Bogachev2001a,
5210 author = {Bogachev, Vladimir I. and R\"{o}ckner, Michael and Wang, Feng-Yu},
5211 doi = {10.1016/S0021-7824(00)01187-9},
5212 file = {::},
5213 issn = {00217824},
5214 journal = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es},
5215 keywords = {53c21,53c80,58b99,58g03,58g32,60j60,82b05,82b21,ams classification,diffusions on manifolds,elliptic equations for measures,functions,gibbs distributions,invariant measures,logarithmic gradients,lyapunov,primary,secondary},
5216 month = mar,
5217 number = {2},
5218 pages = {177--221},
5219 title = {{Elliptic equations for invariant measures on finite and infinite dimensional manifolds}},
5220 url = {http://linkinghub.elsevier.com/retrieve/pii/S0021782400011879},
5221 volume = {80},
5222 year = {2001}
5223 }
5224 @article{gotts2007,
5225 author = {Gotts, N.M.},
5226 file = {::},
5227 journal = {Ecology and Society},
5228 keywords = {adaptive cycle,cross-scale interaction,panarchy,population,resilience,technology,world-},
5229 number = {1},
5230 pages = {24},
5231 title = {{Resilience, panarchy, and world-systems analysis}},
5232 url = {http://www.philadelphia.edu.jo/courses/SAD/ES-2007-2017.pdf},
5233 volume = {12},
5234 year = {2007}
5235 }
5236 @article{Korzec2007,
5237 author = {Korzec, M.D. and Evans, P.L. and M\"{u}nch, A. and Wagner, B},
5238 file = {::},
5239 journal = {Arxiv preprint arXiv:0712.2482},
5240 keywords = {convective cahn-hilliard,dynamical systems,exponential asymptotics,matching,quantum dots},
5241 pages = {1--32},
5242 title = {{Stationary solutions of driven fourth-and sixth-order Cahn-Hilliard type equations}},
5243 url = {http://arxiv.org/abs/0712.2482},
5244 year = {2007}
5245 }
5246 @article{Zitt2008,
5247 author = {Zitt, Pierre-Andr\'{e}},
5248 doi = {10.1016/j.spa.2007.04.002},
5249 file = {::},
5250 issn = {03044149},
5251 journal = {Stochastic Processes and their Applications},
5252 keywords = {capacity criterion,e inequality,measure,simulated annealing,weak poincar},
5253 month = jan,
5254 number = {1},
5255 pages = {76--119},
5256 title = {{Annealing diffusions in a potential function with a slow growth}},
5257 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414907000555},
5258 volume = {118},
5259 year = {2008}
5260 }
5261 @article{Hirsch1984,
5262 author = {Hirsch, M.W.},
5263 file = {::},
5264 journal = {Bull, American Mathematical Society},
5265 number = {1},
5266 pages = {1--64},
5267 title = {{The dynamical systems approach to differential equations}},
5268 url = {http://www.ams.org/journals/bull/1984-11-01/S0273-0979-1984-15236-4/S0273-0979-1984-15236-4.pdf},
5269 volume = {11},
5270 year = {1984}
5271 }
5272 @article{Kawabi2005,
5273 author = {Kawabi, Hiroshi},
5274 file = {::},
5275 journal = {Potential Analysis},
5276 keywords = {gradient estimate,parabolic harnack inequality,spde,varadhan type small time},
5277 number = {1},
5278 pages = {61--84},
5279 publisher = {Springer},
5280 title = {{The parabolic Harnack inequality for the time dependent Ginzburg–Landau type SPDE and its application}},
5281 url = {http://www.springerlink.com/index/R255173448J35035.pdf},
5282 volume = {22},
5283 year = {2005}
5284 }
5285 @article{Berglund2007c,
5286 archivePrefix = {arXiv},
5287 arxivId = {arXiv:math/0611648v2},
5288 author = {Berglund, Nils and Fernandez, Bastien and Gentz, Barbara},
5289 eprint = {0611648v2},
5290 file = {::;::},
5291 journal = {Nonlinearity},
5292 keywords = {and phrases,chronisation,diffusive coupling,ginzburg,interacting diffusions,landau spde,large deviations,lattice dynamical systems,metastability,most probable transition,most probable transition paths,open systems,paths,spatially extended systems,stochastic differential equations,symmetry groups,symplectic twist maps,syn-,synchronisation,transitions times,wentzell-freidlin theory},
5293 pages = {2583},
5294 primaryClass = {arXiv:math},
5295 publisher = {IOP Publishing},
5296 title = {{Metastability in interacting nonlinear stochastic differential equations: II. Large-N behaviour}},
5297 url = {http://iopscience.iop.org/0951-7715/20/11/006 http://iopscience.iop.org/0951-7715/20/11/007},
5298 volume = {20},
5299 year = {2007}
5300 }
5301 @article{Kolmogorov1983,
5302 author = {Kolmogorov, A},
5303 file = {::},
5304 journal = {Probability theory and mathematical statistics},
5305 title = {{On logical foundations of probability theory}},
5306 url = {http://www.springerlink.com/index/C280G6665G4MH441.pdf},
5307 year = {1983}
5308 }
5309 @book{VandenBerg2003,
5310 author = {van den Berg, J. B. and Vandervorst, R. C. and Ghrist, R. W.},
5311 booktitle = {Inventiones Mathematicae},
5312 doi = {10.1007/s00222-002-0277-0},
5313 file = {::},
5314 isbn = {0022200202770},
5315 issn = {0020-9910},
5316 month = may,
5317 number = {2},
5318 pages = {369--432},
5319 title = {{Morse theory on spaces of braids and Lagrangian dynamics}},
5320 url = {http://www.springerlink.com/Index/10.1007/s00222-002-0277-0},
5321 volume = {152},
5322 year = {2003}
5323 }
5324 @article{Liu2003,
5325 author = {Liu, D.},
5326 file = {::},
5327 journal = {Communications in Mathematical Sciences},
5328 keywords = {ginzburg-landau equation,rate of convergence,space-time white noise,spectral method,stochastic partial differential equa-,tions},
5329 number = {2},
5330 pages = {361--375},
5331 publisher = {International Press of Boston},
5332 title = {{Convergence of the spectral method for stochastic Ginzburg-Landau equation driven by space-time white noise}},
5333 url = {http://projecteuclid.org/euclid.cms/1118152076},
5334 volume = {1},
5335 year = {2003}
5336 }
5337 @article{assaf.meerson10,
5338 archivePrefix = {arXiv},
5339 arxivId = {arXiv:0907.0070v3},
5340 author = {Assaf, Michael and Meerson, Baruch},
5341 eprint = {arXiv:0907.0070v3},
5342 file = {::},
5343 journal = {Physical Review E},
5344 number = {2},
5345 pages = {021116},
5346 publisher = {APS},
5347 title = {{Extinction of metastable stochastic populations}},
5348 url = {http://pre.aps.org/abstract/PRE/v81/i2/e021116},
5349 volume = {81},
5350 year = {2010}
5351 }
5352 @article{Budhiraja2008,
5353 author = {Budhiraja, Amarjit and Dupuis, Paul and Maroulas, Vasileios},
5354 doi = {10.1214/07-AOP362},
5355 file = {::},
5356 issn = {0091-1798},
5357 journal = {The Annals of Probability},
5358 month = jul,
5359 number = {4},
5360 pages = {1390--1420},
5361 title = {{Large deviations for infinite dimensional stochastic dynamical systems}},
5362 url = {http://projecteuclid.org/euclid.aop/1217360973},
5363 volume = {36},
5364 year = {2008}
5365 }
5366 @article{lelievre12,
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5368 file = {::},
5369 journal = {Arxiv preprint arXiv:1201.3775},
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5374 }
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5376 author = {Paine, JW and Hoog, FR},
5377 file = {::},
5378 journal = {Computing},
5379 pages = {123--139},
5380 title = {{On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems}},
5381 url = {http://www.springerlink.com/index/Y63P073789N33840.pdf},
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5383 year = {1981}
5384 }
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5389 }
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5392 file = {::},
5393 journal = {Physica D: Nonlinear Phenomena},
5394 keywords = {charge-density wave,f noise,hierarchy,l,spin-glass,vortex noise},
5395 number = {2-4},
5396 pages = {421--429},
5397 publisher = {Elsevier},
5398 title = {{Sorting out landscapes by mesoscopic noise}},
5399 url = {http://www.sciencedirect.com/science/article/pii/S0167278997001103},
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5406 journal = {AMERICAN MATHEMATICAL SOCIETY},
5407 number = {1},
5408 pages = {49--52},
5409 title = {{Bifurcation and stability for a nonlinear parabolic partial differential equation}},
5410 url = {http://www.ams.org/journals/bull/1974-80-01/S0002-9904-1974-13349-5/S0002-9904-1974-13349-5.pdf},
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5418 issn = {0305-4470},
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5420 month = apr,
5421 number = {15},
5422 pages = {L237--L246},
5423 title = {{L\'{e}vy flights: transitions and meta-stability}},
5424 url = {http://stacks.iop.org/0305-4470/39/i=15/a=L01?key=crossref.f804f9c4a34272b0d15b78e8a53997ea},
5425 volume = {39},
5426 year = {2006}
5427 }
5428 @article{Hairer2011a,
5429 archivePrefix = {arXiv},
5430 arxivId = {arXiv:1008.1708v1},
5431 author = {Hairer, M.},
5432 doi = {10.1002/cpa.20383},
5433 eprint = {arXiv:1008.1708v1},
5434 file = {::;::},
5435 issn = {00103640},
5436 journal = {Communications on Pure and Applied Mathematics},
5437 month = jul,
5438 pages = {n/a--n/a},
5439 title = {{Rough stochastic PDEs}},
5440 url = {http://doi.wiley.com/10.1002/cpa.20383},
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5442 }
5443 @article{JKO97,
5444 author = {Jordan, Richard and Kinderlehrer, David and Otto, Felix},
5445 file = {::},
5446 journal = {Physica D: Nonlinear Phenomena},
5447 keywords = {- s is the,1,e,entropy and,f,f l - i,fokker-planck equation,free energy,functional of the form,gradient flux,in terms,introduction and overview,many important questions in,of a free energy,potential energy,processes may be cast,s,statistical mechanics and in,the theory of stochastic,wasserstein metric,where e is the},
5448 pages = {265--271},
5449 title = {{Free energy and the Fokker-Planck equation}},
5450 url = {http://www.sciencedirect.com/science/article/pii/S0167278997000936},
5451 volume = {107},
5452 year = {1997}
5453 }
5454 @article{Neiman-Zade1999,
5455 author = {Neiman-Zade, MI and Shkalikov, A. A.},
5456 file = {::},
5457 journal = {Mathematical Notes},
5458 keywords = {distribution,generalized function,laplace operator,point interaction,polyharmonic operator,resolvent identities,schrhdinger operator,singular perturbation},
5459 number = {5},
5460 pages = {599--607},
5461 publisher = {Springer},
5462 title = {{Schr\"{o}dinger operators with singular potentials from the space of multiplicators}},
5463 url = {http://www.springerlink.com/index/96842604585N5M43.pdf},
5464 volume = {66},
5465 year = {1999}
5466 }
5467 @article{Day1990,
5468 author = {Day, Martin V.},
5469 doi = {10.1016/0022-247X(90)90389-W},
5470 file = {::},
5471 issn = {0022247X},
5472 journal = {Journal of Mathematical Analysis and Applications},
5473 month = mar,
5474 number = {1},
5475 pages = {134--153},
5476 title = {{Large deviations results for the exit problem with characteristic boundary}},
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5478 volume = {147},
5479 year = {1990}
5480 }
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5482 author = {Guerra, F. and Rosen, L and Simon, Barry},
5483 file = {::},
5484 journal = {The Annals of Mathematics},
5485 number = {1},
5486 pages = {111--189},
5487 publisher = {JSTOR},
5488 title = {{The $P (\varphi)_2$ Euclidean quantum field theory as classical statistical mechanics}},
5489 url = {http://www.jstor.org/stable/10.2307/1970988},
5490 volume = {101},
5491 year = {1975}
5492 }
5493 @misc{Kuksin2011,
5494 author = {Kuksin, Sergei},
5495 booktitle = {Quantum},
5496 file = {::},
5497 pages = {1--16},
5498 title = {{Quantum averaging , quantum KAM and quantum diffusion .}},
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5502 author = {Farmer, C},
5503 doi = {10.1016/0022-247X(71)90172-7},
5504 file = {::},
5505 issn = {0022247X},
5506 journal = {Journal of Mathematical Analysis and Applications},
5507 month = apr,
5508 number = {1},
5509 pages = {228--232},
5510 title = {{A certain sequence of infinite determinants}},
5511 url = {http://linkinghub.elsevier.com/retrieve/pii/0022247X71901727},
5512 volume = {34},
5513 year = {1971}
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5517 doi = {10.1016/j.spa.2010.03.006},
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5519 issn = {03044149},
5520 journal = {Stochastic Processes and their Applications},
5521 keywords = {metastability,nonlinear perturbations},
5522 month = jul,
5523 number = {7},
5524 pages = {1194--1214},
5525 publisher = {Elsevier B.V.},
5526 title = {{Metastability for nonlinear random perturbations of dynamical systems}},
5527 url = {http://linkinghub.elsevier.com/retrieve/pii/S030441491000075X},
5528 volume = {120},
5529 year = {2010}
5530 }
5531 @article{Serfaty2009,
5532 author = {Serfaty, Sylvia},
5533 file = {::},
5534 journal = {Comm. Appl. Nonlinear Anal., to appear},
5535 pages = {1--30},
5536 title = {{Gamma-convergence of gradient flows on Hilbert and metric spaces and applications}},
5537 url = {http://www.ann.jussieu.fr/serfaty/gcv-erice2.pdf},
5538 year = {2009}
5539 }
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5541 author = {Brassesco, Stella},
5542 file = {::},
5543 journal = {Stochastic processes and their applications},
5544 pages = {33--53},
5545 title = {{Some results on small random perturbations of an infinite dimensional dynamical system}},
5546 url = {http://www.sciencedirect.com/science/article/pii/030441499190071J},
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5549 }
5550 @book{davies89,
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5552 pages = {x+197},
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5555 year = {1989}
5556 }
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5559 doi = {10.1016/j.jde.2007.03.007},
5560 file = {::},
5561 issn = {00220396},
5562 journal = {Journal of Differential Equations},
5563 keywords = {coarsening rates,dynamic metastability,energy methods,nonlinear partial differential equations},
5564 month = jun,
5565 number = {2},
5566 pages = {372--420},
5567 title = {{Slow motion of gradient flows}},
5568 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039607000824},
5569 volume = {237},
5570 year = {2007}
5571 }
5572 @article{Voros1982,
5573 author = {Voros, A.},
5574 file = {::},
5575 title = {{Spectre de l'equation de schrodinger et methode BKW}},
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5581 doi = {10.1016/j.jfa.2006.04.015},
5582 file = {::},
5583 issn = {00221236},
5584 journal = {Journal of Functional Analysis},
5585 keywords = {eigenvalue asymptotics,liouville operators,singular potentials,sturm},
5586 month = sep,
5587 number = {1},
5588 pages = {27--57},
5589 title = {{Eigenvalue asymptotics for Sturm–Liouville operators with singular potentials}},
5590 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123606001844},
5591 volume = {238},
5592 year = {2006}
5593 }
5594 @article{Cattiaux2010b,
5595 author = {Cattiaux, Patrick and Guillin, Arnaud},
5596 file = {::},
5597 keywords = {26d10,47d07,60g10,60j60,e inequality,logarithmic sobolev inequality,lyapunov condition,msc 2000,poincar,transportation information inequality},
5598 pages = {1--11},
5599 title = {{Functional Inequalities via Lyapunov conditions}},
5600 url = {http://hal.archives-ouvertes.fr/docs/00/44/61/04/PDF/cg-procgrenoble_2.pdf},
5601 year = {2010}
5602 }
5603 @article{wolfrum02,
5604 author = {Wolfrum, Matthias},
5605 file = {::},
5606 journal = {Journal of Dynamics and Differential Equations},
5607 keywords = {attractors,heteroclinic orbits,meandric permutations,morse-smale systems,nodal properties,scalar semilinear equations},
5608 number = {1},
5609 pages = {207--241},
5610 title = {{Geometry of heteroclinic cascades in scalar parabolic differential equations}},
5611 url = {http://www.springerlink.com/index/X00M5X50564071M7.pdf},
5612 volume = {14},
5613 year = {2002}
5614 }
5615 @article{Berglund2001a,
5616 archivePrefix = {arXiv},
5617 arxivId = {arXiv:math/0111178v1},
5618 author = {Berglund, Nils},
5619 eprint = {0111178v1},
5620 file = {::},
5621 journal = {Arxiv preprint math/0111178},
5622 primaryClass = {arXiv:math},
5623 title = {{Perturbation theory of dynamical systems}},
5624 url = {http://arxiv.org/abs/math/0111178},
5625 year = {2001}
5626 }
5627 @article{Ge2006,
5628 author = {Ge, Hao and Jiang, Da-Quan and Qian, Min},
5629 doi = {10.1007/s10955-006-9099-6},
5630 file = {::},
5631 issn = {0022-4715},
5632 journal = {Journal of Statistical Physics},
5633 keywords = {brownian motor,circulation,detailed balance,entropy production,fluctuation theorem,periodical reversibility,time-periodic markov chain},
5634 month = jun,
5635 number = {4},
5636 pages = {831--859},
5637 title = {{A Simple Discrete Model of Brownian Motors: Time-periodic Markov Chains}},
5638 url = {http://www.springerlink.com/index/10.1007/s10955-006-9099-6},
5639 volume = {123},
5640 year = {2006}
5641 }
5642 @article{LeGall1994,
5643 author = {{Le Gall}, Jean-Fran\c{c}ois},
5644 file = {::},
5645 journal = {Ann. Inst. Four},
5646 pages = {277--306},
5647 title = {{Hitting probabilities and potential theory for the Brownian path-valued process}},
5648 url = {http://archive.numdam.org/article/AIF_1994__44_1_277_0.pdf},
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5650 year = {1994}
5651 }
5652 @article{Gyongy1999,
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5654 file = {::},
5655 journal = {The Annals of Probability},
5656 number = {2},
5657 pages = {782--802},
5658 publisher = {Institute of Mathematical Statistics},
5659 title = {{ON THE STOCHASTIC BURGERS ’ EQUATION IN THE REAL LINE}},
5660 url = {http://projecteuclid.org/euclid.aop/1022677386},
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5662 year = {1999}
5663 }
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5665 author = {Martinelli, Fabio and Olivieri, Enzo and Scoppola, Elisabetta},
5666 file = {::},
5667 journal = {Journal of Statistical Physics},
5668 keywords = {1,consider some problems arising,dynamical systems,exit times,i n t r,in the study of,in this paper we,o d u c,small,small random perturbations,t i o n},
5669 number = {3},
5670 pages = {477--504},
5671 publisher = {Springer},
5672 title = {{Small random perturbations of finite-and infinite-dimensional dynamical systems: unpredictability of exit times}},
5673 url = {http://www.springerlink.com/index/M307207261100V64.pdf},
5674 volume = {55},
5675 year = {1989}
5676 }
5677 @article{Hairer2008a,
5678 author = {Hairer, Martin and Mattingly, Jonathan C.},
5679 file = {::},
5680 journal = {Electronic Journal of Probability},
5681 pages = {658--738},
5682 title = {{A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs}},
5683 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/include/getdoc4164.pdf?id=5978&article=2206&mode=pdf},
5684 volume = {16},
5685 year = {2008}
5686 }
5687 @article{brunovsky.polacik97,
5688 author = {Brunovsky, P. and Pol\'{a}cik, P.},
5689 file = {::},
5690 journal = {Journal of differential equations},
5691 number = {1},
5692 pages = {129--181},
5693 publisher = {Academic Press},
5694 title = {{The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension}},
5695 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=10168512},
5696 volume = {135},
5697 year = {1997}
5698 }
5699 @misc{TheMendeleySupportTeam2011,
5700 abstract = {A quick introduction to Mendeley. Learn how Mendeley creates your personal digital library, how to organize and annotate documents, how to collaborate and share with colleagues, and how to generate citations and bibliographies.},
5701 address = {London},
5702 author = {{The Mendeley Support Team}},
5703 booktitle = {Mendeley Desktop},
5704 file = {::},
5705 keywords = {Mendeley,how-to,user manual},
5706 pages = {1--16},
5707 publisher = {Mendeley Ltd.},
5708 title = {{Getting Started with Mendeley}},
5709 url = {http://www.mendeley.com},
5710 year = {2011}
5711 }
5712 @article{Pacard2011,
5713 archivePrefix = {arXiv},
5714 arxivId = {arXiv:1102.3446v1},
5715 author = {Pacard, Frank and Wei, Juncheng},
5716 eprint = {arXiv:1102.3446v1},
5717 file = {::},
5718 journal = {Arxiv preprint arXiv:1102.3446},
5719 keywords = {allen-cahn equation,and phrases,infinite-,multiple-end solutions,toda system},
5720 pages = {1--30},
5721 title = {{Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones}},
5722 url = {http://arxiv.org/abs/1102.3446},
5723 year = {2011}
5724 }
5725 @article{VandenBerg2011,
5726 author = {van den Berg, J. B. and Kram\'{a}r, M. and Vandervorst, R. C.},
5727 file = {::},
5728 journal = {SIAM Journal on Applied Dynamical Systems},
5729 keywords = {1,10,100796558,1137,34c12,49jxx,49s05,70hxx,70kxx,ams subject classifications,as hamil-,conley index,doi,fourth order conservative dynamical,fourth order equations,introduction,parabolic recurrence relations,relative braid classes,systems can be viewed},
5730 number = {2},
5731 pages = {510},
5732 title = {{The Order of Bifurcation Points in Fourth Order Conservative Systems via Braids}},
5733 url = {http://www.few.vu.nl/$\sim$RCAM.van.der.Vorst/PAPERS/BKV-2.pdf},
5734 volume = {10},
5735 year = {2011}
5736 }
5737 @article{Eckmann2001d,
5738 author = {Eckmann, J.-P. and Hairer, Martin},
5739 file = {::},
5740 journal = {Nonlinearity},
5741 number = {133},
5742 title = {{Invariant measures for stochastic partial differential}},
5743 volume = {14},
5744 year = {2001}
5745 }
5746 @article{Cattiaux2009,
5747 author = {Cattiaux, Patrick and Collet, Pierre and Lambert, Amaury and Mart\'{\i}nez, Servet and M\'{e}l\'{e}ard, Sylvie and {San Mart\'{\i}n}, Jaime},
5748 doi = {10.1214/09-AOP451},
5749 file = {::},
5750 issn = {0091-1798},
5751 journal = {The Annals of Probability},
5752 month = sep,
5753 number = {5},
5754 pages = {1926--1969},
5755 title = {{Quasi-stationary distributions and diffusion models in population dynamics}},
5756 url = {http://projecteuclid.org/euclid.aop/1253539860},
5757 volume = {37},
5758 year = {2009}
5759 }
5760 @article{kramers40,
5761 author = {Kramers, HA},
5762 file = {::},
5763 journal = {Physica},
5764 title = {{Brownian motion in a field of force and the diffusion model of chemical reactions}},
5765 url = {http://www.sciencedirect.com/science/article/pii/S0031891440900982},
5766 year = {1940}
5767 }
5768 @article{Bakhtin2007,
5769 author = {Bakhtin, Yuri and Mattingly, Jonathan C.},
5770 doi = {10.1016/j.jfa.2007.02.011},
5771 file = {::},
5772 issn = {00221236},
5773 journal = {Journal of Functional Analysis},
5774 keywords = {degenerate stochastic partial differential,equations,malliavin calculus,smooth densities,spdes,stochastic},
5775 month = aug,
5776 number = {2},
5777 pages = {307--353},
5778 title = {{Malliavin calculus for infinite-dimensional systems with additive noise}},
5779 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123607000559},
5780 volume = {249},
5781 year = {2007}
5782 }
5783 @article{Hairer2008b,
5784 author = {Hairer, Martin and Pardoux, Etienne},
5785 doi = {10.1016/j.jfa.2008.04.014},
5786 file = {::},
5787 issn = {00221236},
5788 journal = {Journal of Functional Analysis},
5789 keywords = {0022-1236,2008 elsevier inc,ac,all rights reserved,cmi,corresponding author,degenerate,e,e-mail addresses,effective diffusivity,fr,hairer,homogenization,m,malliavin calculus,pardoux,see front matter,spectral gap,uk,univ-mrs,warwick},
5790 month = nov,
5791 number = {9},
5792 pages = {2462--2487},
5793 publisher = {Elsevier Inc.},
5794 title = {{Homogenization of periodic linear degenerate PDEs}},
5795 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123608001699},
5796 volume = {255},
5797 year = {2008}
5798 }
5799 @article{Albeverio2004,
5800 author = {Albeverio, Sergio and Mazzucchi, S.},
5801 file = {::},
5802 journal = {Journal of statistical physics},
5803 keywords = {as a small sign,birthday,convoluted poisson noise,euclidean,feynman path integrals,it is a great,occasion of his 70th,of deep gratitude,on the,paper to gianni jona-lasinio,pleasure to dedicate this,poisson random fields,quantum fields,schr\"{o}dinger equation},
5804 number = {1},
5805 pages = {191--215},
5806 publisher = {Springer},
5807 title = {{Some new developments in the theory of path integrals, with applications to quantum theory}},
5808 url = {http://www.springerlink.com/index/N85781GRQ00507H3.pdf},
5809 volume = {115},
5810 year = {2004}
5811 }
5812 @article{Morato2011,
5813 author = {Morato, L.M. and Ugolini, Stefania},
5814 file = {::},
5815 pages = {1--14},
5816 publisher = {Taylor & Francis},
5817 title = {{Stochastic quantization of finite dimensional systems with electromagnetic interactions}},
5818 url = {http://www.tandfonline.com/doi/abs/10.1080/17442508.2010.512975},
5819 year = {2011}
5820 }
5821 @misc{Pakin2009,
5822 author = {Pakin, Scott},
5823 booktitle = {Network},
5824 file = {::},
5825 number = {November},
5826 title = {{The comprehensive LATEX symbol list}},
5827 url = {http://jamsb.austms.org.au/resources/LaTeX/symbols-a4.pdf},
5828 year = {2009}
5829 }
5830 @article{Ferrari2011,
5831 archivePrefix = {arXiv},
5832 arxivId = {arXiv:1104.2129v1},
5833 author = {Ferrari, Patrik L. and Frings, Ren\'{e}},
5834 eprint = {arXiv:1104.2129v1},
5835 file = {::},
5836 journal = {Journal of Statistical Physics},
5837 pages = {1--28},
5838 publisher = {Springer},
5839 title = {{Finite time corrections in KPZ growth models}},
5840 url = {http://www.springerlink.com/index/N435757L2278270K.pdf},
5841 year = {2011}
5842 }
5843 @article{E2006,
5844 author = {E, Weinan and Vanden-Eijnden, Eric},
5845 doi = {10.1007/s10955-005-9003-9},
5846 file = {::},
5847 issn = {0022-4715},
5848 journal = {Journal of Statistical Physics},
5849 keywords = {between long lived states,biology,but important transition events,chemistry,etc,is dominated by rare,many systems arising in,matastability,physics,reactive trajectories,the dynamical behavior of,transition path sampling,transition path theory,transition pathways,transition state theory},
5850 month = may,
5851 number = {3},
5852 pages = {503--523},
5853 title = {{Towards a Theory of Transition Paths}},
5854 url = {http://www.springerlink.com/index/10.1007/s10955-005-9003-9},
5855 volume = {123},
5856 year = {2006}
5857 }
5858 @article{Doss1978,
5859 author = {Doss, H and Royer, G},
5860 file = {::},
5861 journal = {Probability Theory and Related Fields},
5862 number = {1},
5863 pages = {107--124},
5864 publisher = {Springer},
5865 title = {{Processus de diffusion associe aux mesures de Gibbs sur $R^{Z^d}$}},
5866 url = {http://www.springerlink.com/index/K203145467714550.pdf},
5867 volume = {46},
5868 year = {1978}
5869 }
5870 @article{Maragliano2006,
5871 abstract = {A computational technique is proposed which combines the string method with a sampling technique to determine minimum free energy paths. The technique only requires to compute the mean force and another conditional expectation locally along the string, and therefore can be applied even if the number of collective variables kept in the free energy calculation is large. This is in contrast with other free energy sampling techniques which aim at mapping the full free energy landscape and whose cost increases exponentially with the number of collective variables kept in the free energy. Provided that the number of collective variables is large enough, the new technique captures the mechanism of transition in that it allows to determine the committor function for the reaction and, in particular, the transition state region. The new technique is illustrated on the example of alanine dipeptide, in which we compute the minimum free energy path for the isomerization transition using either two or four dihedral angles as collective variables. It is shown that the mechanism of transition can be captured using the four dihedral angles, but it cannot be captured using only two of them.},
5872 author = {Maragliano, Luca and Fischer, Alexander and Vanden-Eijnden, Eric and Ciccotti, Giovanni},
5873 doi = {10.1063/1.2212942},
5874 file = {::},
5875 issn = {0021-9606},
5876 journal = {The Journal of chemical physics},
5877 month = jul,
5878 number = {2},
5879 pages = {24106},
5880 pmid = {16848576},
5881 title = {{String method in collective variables: minimum free energy paths and isocommittor surfaces.}},
5882 url = {http://www.ncbi.nlm.nih.gov/pubmed/16848576},
5883 volume = {125},
5884 year = {2006}
5885 }
5886 @article{Quer-Sardanyons2006,
5887 author = {Quer-Sardanyons, Llu\'{\i}s and Sanz-Sol\'{e}, Marta},
5888 doi = {10.1007/s11118-005-9002-0},
5889 file = {::},
5890 issn = {0926-2601},
5891 journal = {Potential Analysis},
5892 keywords = {discretisation schemes,stochastic partial differential equations,wave equation},
5893 month = may,
5894 number = {4},
5895 pages = {303--332},
5896 title = {{Space Semi-Discretisations for a Stochastic Wave Equation}},
5897 url = {http://www.springerlink.com/index/10.1007/s11118-005-9002-0},
5898 volume = {24},
5899 year = {2006}
5900 }
5901 @article{Valent1985,
5902 author = {Valent, V.},
5903 file = {::},
5904 journal = {Rend. Sem. Mat. Univ. Padova},
5905 pages = {63--73},
5906 title = {{A property of multiplication in Sobolev spaces. Some applications}},
5907 url = {http://archive.numdam.org/article/RSMUP_1985__74__63_0.pdf},
5908 volume = {74},
5909 year = {1985}
5910 }
5911 @article{Ryser2011,
5912 archivePrefix = {arXiv},
5913 arxivId = {arXiv:1104.0720v2},
5914 author = {Ryser, Marc D. and Nigam, Nilima and Tupper, Paul F.},
5915 eprint = {arXiv:1104.0720v2},
5916 file = {::;::},
5917 keywords = {allen-cahn equation,numerical,stochastic pdes,well-posedness,white noise},
5918 pages = {1--20},
5919 title = {{On the well-posedness of the stochastic Allen-Cahn equation in two dimensions}},
5920 year = {2011}
5921 }
5922 @article{Funaki2004b,
5923 author = {Funaki, Tadahisa},
5924 doi = {10.1214/009117904000000180},
5925 file = {::},
5926 issn = {0091-1798},
5927 journal = {The Annals of Probability},
5928 month = apr,
5929 number = {2},
5930 pages = {1201--1227},
5931 title = {{Zero temperature limit for interacting Brownian particles. I. Motion of a single body}},
5932 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884849/},
5933 volume = {32},
5934 year = {2004}
5935 }
5936 @article{BV97,
5937 author = {Baviera, R. and Virasoro, M.a.},
5938 doi = {10.1016/S0167-2789(97)00079-1},
5939 file = {::},
5940 issn = {01672789},
5941 journal = {Physica D: Nonlinear Phenomena},
5942 keywords = {gibbs-boltzmann partition function,hierarchical landscapes,hypersurface,multiscale analysis,replica formalism,rugged energy,tap solutions},
5943 month = sep,
5944 number = {2-4},
5945 pages = {151--155},
5946 title = {{Multiscale analysis of hierarchical landscapes}},
5947 url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278997000791},
5948 volume = {107},
5949 year = {1997}
5950 }
5951 @article{Sugiura1996,
5952 author = {Sugiura, Makoto},
5953 file = {::},
5954 journal = {Nagoya Mathematical Journal},
5955 pages = {137--154},
5956 title = {{Exponential asymptotics in the small parameter exit problem}},
5957 url = {http://projecteuclid.org/euclid.nmj/1118771877},
5958 volume = {144},
5959 year = {1996}
5960 }
5961 @article{Bianconi2010,
5962 archivePrefix = {arXiv},
5963 arxivId = {arXiv:1011.1523v1},
5964 author = {Bianconi, Ginestra and Rahmede, Christoph},
5965 eprint = {arXiv:1011.1523v1},
5966 file = {::},
5967 journal = {Arxiv preprint arXiv:1011.1523},
5968 number = {1},
5969 pages = {1--8},
5970 title = {{Quantum mechanical formalism for biological evolution}},
5971 url = {http://arxiv.org/abs/1011.1523},
5972 year = {2010}
5973 }
5974 @book{freidlin.wentzell84,
5975 author = {Freidlin, Mark I. and Wentzell, AD},
5976 edition = {Grundlehre},
5977 pages = {viii+326},
5978 publisher = {Springer-Verlag},
5979 title = {{Random perturbations of dynamical systems}},
5980 year = {1984}
5981 }
5982 @article{Smirnov2010,
5983 archivePrefix = {arXiv},
5984 arxivId = {arXiv:1009.6077v1},
5985 author = {Smirnov, Stanislav},
5986 eprint = {arXiv:1009.6077v1},
5987 file = {::},
5988 journal = {Arxiv preprint arXiv:1009.6077},
5989 keywords = {avoiding walk,conformal invariance,discrete analytic function,discrete complex analysis,ising model,self-},
5990 title = {{Discrete complex analysis and probability}},
5991 url = {http://arxiv.org/abs/1009.6077},
5992 year = {2010}
5993 }
5994 @book{port.stone78,
5995 author = {Port, Sidney C. and Stone, Charles J.},
5996 pages = {xii+236},
5997 publisher = {Academic Press},
5998 title = {{Brownian motion and classical potential theory}},
5999 year = {1978}
6000 }
6001 @article{Ren2005,
6002 abstract = {The finite-temperature string method proposed by E, et al. [W. E, W. Ren, and E. Vanden-Eijnden, Phys. Rev. B 66, 052301 (2002)] is a very effective way of identifying transition mechanisms and transition rates between metastable states in systems with complex energy landscapes. In this paper, we discuss the theoretical background and algorithmic details of the finite-temperature string method, as well as the application to the study of isomerization reaction of the alanine dipeptide, both in vacuum and in explicit solvent. We demonstrate that the method allows us to identify directly the isocommittor surfaces, which are approximated by hyperplanes, in the region of configuration space where the most probable transition trajectories are concentrated. These results are verified subsequently by computing directly the committor distribution on the hyperplanes that define the transition state region.},
6003 author = {Ren, Weiqing and Vanden-Eijnden, Eric and Maragakis, Paul and E, Weinan},
6004 doi = {10.1063/1.2013256},
6005 file = {::},
6006 issn = {0021-9606},
6007 journal = {The Journal of chemical physics},
6008 keywords = {Alanine,Alanine: chemistry,Algorithms,Computer Simulation,Dipeptides,Dipeptides: chemistry,Isomerism,Models, Chemical,Models, Molecular,Molecular Conformation,Temperature,Thermodynamics},
6009 month = oct,
6010 number = {13},
6011 pages = {134109},
6012 pmid = {16223277},
6013 title = {{Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide.}},
6014 url = {http://www.ncbi.nlm.nih.gov/pubmed/16223277},
6015 volume = {123},
6016 year = {2005}
6017 }
6018 @article{MSS94,
6019 author = {Martinelli, F. and Sbano, L. and Scoppola, E.},
6020 journal = {Stochastics Stochastics Rep.},
6021 number = {3-4},
6022 pages = {253----272},
6023 title = {{Small random perturbation of dynamical systems: recursive multiscale analysis}},
6024 volume = {49},
6025 year = {1994}
6026 }
6027 @article{Eckmann2001e,
6028 author = {Eckmann, J-p and Hairer, M},
6029 file = {::},
6030 journal = {Nonlinearity},
6031 pages = {133},
6032 publisher = {IOP Publishing},
6033 title = {{Invariant measures for stochastic partial differential equations in unbounded domains}},
6034 url = {http://iopscience.iop.org/0951-7715/14/1/308},
6035 volume = {14},
6036 year = {2001}
6037 }
6038 @article{Hinz2009a,
6039 author = {Hinz, Michael and Z\"{a}hle, Martina},
6040 doi = {10.1016/j.jfa.2009.02.006},
6041 file = {::},
6042 issn = {00221236},
6043 journal = {Journal of Functional Analysis},
6044 keywords = {fractional brownian sheet,fractional calculus,semigroups,stochastic partial differential equations},
6045 month = may,
6046 number = {10},
6047 pages = {3192--3235},
6048 publisher = {Elsevier Inc.},
6049 title = {{Gradient type noises II – Systems of stochastic partial differential equations}},
6050 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123609000706},
6051 volume = {256},
6052 year = {2009}
6053 }
6054 @article{Chekroun2011,
6055 author = {Chekroun, Micka\"{e}l D. and Simonnet, Eric and Ghil, Michael},
6056 doi = {10.1016/j.physd.2011.06.005},
6057 file = {::},
6058 issn = {01672789},
6059 journal = {Physica D: Nonlinear Phenomena},
6060 month = oct,
6061 number = {21},
6062 pages = {1685--1700},
6063 publisher = {Elsevier B.V.},
6064 title = {{Stochastic climate dynamics: Random attractors and time-dependent invariant measures}},
6065 url = {http://linkinghub.elsevier.com/retrieve/pii/S016727891100145X},
6066 volume = {240},
6067 year = {2011}
6068 }
6069 @article{Kleinhans2011,
6070 archivePrefix = {arXiv},
6071 arxivId = {arXiv:1011.1109v1},
6072 author = {Kleinhans, David and Jonsson, P.R.},
6073 eprint = {arXiv:1011.1109v1},
6074 file = {::},
6075 journal = {Journal of Theoretical Biology},
6076 keywords = {connectivity matrix,dispersal network,metapopulation viability,symmetry},
6077 publisher = {Elsevier},
6078 title = {{On the impact of dispersal asymmetry on metapopulation persistence}},
6079 url = {http://www.sciencedirect.com/science/article/pii/S0022519311004589},
6080 year = {2011}
6081 }
6082 @article{Getoor1973,
6083 author = {Getoor, R. K. and Sharpe, M. J.},
6084 file = {::},
6085 journal = {The Annals of Probability},
6086 number = {4},
6087 pages = {1973},
6088 title = {{Last exit times and additive functionals}},
6089 url = {http://projecteuclid.org/euclid.aop/1176996885},
6090 volume = {1},
6091 year = {1973}
6092 }
6093 @article{Hairer2012,
6094 archivePrefix = {arXiv},
6095 arxivId = {arXiv:1202.3094v1},
6096 author = {Hairer, Martin and Maas, Jan and Weber, Hendrik},
6097 eprint = {arXiv:1202.3094v1},
6098 file = {::},
6099 journal = {Society},
6100 pages = {1--75},
6101 title = {{Approximating rough stochastic pdes}},
6102 year = {2012}
6103 }
6104 @misc{Hairer,
6105 author = {Hairer, Martin},
6106 file = {::},
6107 number = {x},
6108 pages = {1--3},
6109 title = {{Ergodic theory for infinite dimensional stochastic processes}}
6110 }
6111 @article{Gilbert2004,
6112 author = {Gilbert, TL},
6113 file = {::},
6114 journal = {Magnetics, IEEE Transactions on},
6115 number = {6},
6116 pages = {3443--3449},
6117 title = {{A phenomenological theory of damping in ferromagnetic materials}},
6118 url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1353448},
6119 volume = {40},
6120 year = {2004}
6121 }
6122 @article{Dalang2007,
6123 author = {Dalang, Robert C. and Khoshnevisan, Davar and Nualart, Eulalia},
6124 file = {::},
6125 journal = {ALEA. Latin American Journal of Probability and Mathematical Statistics},
6126 pages = {231--271},
6127 title = {{Hitting probabilities for systems of non-linear stochastic heat equations with additive noise}},
6128 url = {http://arxiv.org/abs/math/0702710},
6129 volume = {3},
6130 year = {2007}
6131 }
6132 @article{Cattiaux2010d,
6133 author = {Cattiaux, Patrick and Guillin, Arnaud and Roberto, Cyril},
6134 file = {::},
6135 journal = {Electronic},
6136 keywords = {1,26d10,39b62,47d07,60g10,60j60,e inequality,introduction and main results,msc 2010,poincar,rate of convergence},
6137 pages = {1--13},
6138 title = {{Poincar\'{e} inequality and the Lp convergence of semi-groups}},
6139 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/ECP/include/getdocc479.pdf?id=5390&article=2212&mode=pdf},
6140 volume = {2},
6141 year = {2010}
6142 }
6143 @article{Carron2002,
6144 author = {Carron, G},
6145 file = {::},
6146 journal = {American journal of mathematics},
6147 number = {2},
6148 pages = {307--352},
6149 title = {{D\'{e}terminant relatif et la fonction $\Xi$}},
6150 url = {http://www.jstor.org/stable/10.2307/25099116},
6151 volume = {124},
6152 year = {2002}
6153 }
6154 @article{Lachowicz2005,
6155 author = {Lachowicz, Mirosław},
6156 doi = {10.1016/j.jmaa.2005.03.020},
6157 file = {::},
6158 issn = {0022247X},
6159 journal = {Journal of Mathematical Analysis and Applications},
6160 keywords = {diffusion equations,integro-differential equations,ode,population dynamics,reaction,stochastic},
6161 month = jul,
6162 number = {2},
6163 pages = {585--605},
6164 title = {{General population systems. Macroscopic limit of a class of stochastic semigroups}},
6165 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022247X0500209X},
6166 volume = {307},
6167 year = {2005}
6168 }
6169 @article{Dalang2008,
6170 author = {Dalang, Robert C. and Khoshnevisan, Davar and Nualart, Eulalia},
6171 doi = {10.1007/s00440-008-0150-1},
6172 file = {::;::},
6173 issn = {0178-8051},
6174 journal = {Probability Theory and Related Fields},
6175 keywords = {2000,60h15,60j45,hitting probabilities,malliavin calculus,mathematics subject classification,noise,primary,secondary,space-time white,stochastic heat equation},
6176 month = apr,
6177 number = {3-4},
6178 pages = {371--427},
6179 title = {{Hitting probabilities for systems of non-linear stochastic heat equations with multiplicative noise}},
6180 url = {http://www.springerlink.com/index/10.1007/s00440-008-0150-1 http://arxiv.org/abs/math/0702710},
6181 volume = {144},
6182 year = {2008}
6183 }
6184 @article{Doering2003,
6185 author = {Doering, C and Mueller, C and Smereka, P},
6186 doi = {10.1016/S0378-4371(03)00203-6},
6187 file = {::},
6188 issn = {03784371},
6189 journal = {Physica A: Statistical Mechanics and its Applications},
6190 keywords = {1,2,3,equation,fkpp,fkpp equation,introduction and motivation,is one of the,it describes a,kolmogorov,mathematical biology and ecology,most fundamental models in,nonlinear wavefronts,petrovsky,piscunov,stochastic pde,the fisher},
6191 month = jul,
6192 number = {1-2},
6193 pages = {243--259},
6194 title = {{Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality}},
6195 url = {http://linkinghub.elsevier.com/retrieve/pii/S0378437103002036},
6196 volume = {325},
6197 year = {2003}
6198 }
6199 @article{Kong1996,
6200 author = {Kong, Q and Zettl, A},
6201 file = {::},
6202 journal = {Journal of differential equations},
6203 number = {1},
6204 pages = {1--19},
6205 publisher = {New York, Academic Press.},
6206 title = {{Eigenvalues of regular Sturm-Liouville problems}},
6207 url = {http://www.math.niu.edu/SL2/papers/koze96b.pdf},
6208 volume = {131},
6209 year = {1996}
6210 }
6211 @article{Berglund2009,
6212 author = {Berglund, Nils and Gentz, Barbara},
6213 file = {::},
6214 journal = {Journal of Physics A: Mathematical and Theoretical},
6215 pages = {052001},
6216 publisher = {IOP Publishing},
6217 title = {{Anomalous behavior of the Kramers rate at bifurcations in classical field theories}},
6218 url = {http://iopscience.iop.org/1751-8121/42/5/052001},
6219 volume = {42},
6220 year = {2009}
6221 }
6222 @article{Bellettini2007,
6223 author = {Bellettini, G. and {De Masi}, A. and Dirr, Nicolas and Presutti, E.},
6224 file = {::},
6225 journal = {Communications in mathematical physics},
6226 number = {3},
6227 pages = {715--763},
6228 publisher = {Springer},
6229 title = {{Tunneling in two dimensions}},
6230 url = {http://www.springerlink.com/index/7267433G60W1270M.pdf},
6231 volume = {269},
6232 year = {2007}
6233 }
6234 @article{Assaf2007,
6235 archivePrefix = {arXiv},
6236 arxivId = {arXiv:cond-mat/0612157v3},
6237 author = {Assaf, Michael and Meerson, Baruch},
6238 eprint = {0612157v3},
6239 file = {::},
6240 journal = {Physical Review E},
6241 number = {3},
6242 pages = {031122},
6243 primaryClass = {arXiv:cond-mat},
6244 publisher = {APS},
6245 title = {{Spectral theory of metastability and extinction in a branching-annihilation reaction}},
6246 url = {http://pre.aps.org/abstract/PRE/v75/i3/e031122},
6247 volume = {75},
6248 year = {2007}
6249 }
6250 @book{Franchi2011,
6251 author = {Franchi, Jacques and {Le Jan}, Yves},
6252 file = {::},
6253 number = {January},
6254 title = {{Hyperbolic Dynamics and Brownian motions an introduction}},
6255 year = {2011}
6256 }
6257 @article{Wilson2009,
6258 author = {Wilson, P. and Madsen, L.},
6259 file = {::},
6260 title = {{The memoir class}},
6261 url = {http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:The+Memoir+Class#0},
6262 year = {2009}
6263 }
6264 @article{Hairer2011c,
6265 author = {Hairer, M.},
6266 doi = {10.1002/cpa.20383},
6267 file = {::},
6268 issn = {00103640},
6269 journal = {Communications on Pure and Applied Mathematics},
6270 month = jul,
6271 pages = {n/a--n/a},
6272 title = {{Rough stochastic PDEs}},
6273 url = {http://doi.wiley.com/10.1002/cpa.20383},
6274 year = {2011}
6275 }
6276 @article{Fisher1997,
6277 author = {Fisher, Daniel S},
6278 file = {::},
6279 journal = {Physica D},
6280 keywords = {ageing,coarsening,domain walls,landscape,ordering},
6281 pages = {204--217},
6282 title = {{Dynamics and domain walls: is the "landscape paradigm" instructive ?}},
6283 volume = {107},
6284 year = {1997}
6285 }
6286 @article{Dawson1975,
6287 author = {Dawson, DA},
6288 file = {::},
6289 journal = {Journal of Multivariate Analysis},
6290 number = {1},
6291 pages = {1--52},
6292 publisher = {Elsevier},
6293 title = {{Stochastic evolution equations and related measure processes}},
6294 url = {http://www.sciencedirect.com/science/article/pii/0047259X75900548},
6295 volume = {5},
6296 year = {1975}
6297 }
6298 @article{Newman1997,
6299 author = {Newman, MEJ},
6300 file = {::},
6301 journal = {Physica D: Nonlinear Phenomena},
6302 keywords = {1-3,a self-organized,although this sugges-,coevolution,critical,est in the idea,extinction,power laws,process,self-organized criticality,soc,that evolution might be,there has in recent,years been considerable inter-},
6303 number = {2-4},
6304 pages = {293--296},
6305 publisher = {Elsevier},
6306 title = {{Evidence for self-organized criticality in evolution}},
6307 url = {http://www.sciencedirect.com/science/article/pii/S0167278997000961},
6308 volume = {107},
6309 year = {1997}
6310 }
6311 @article{Freidlin1988,
6312 author = {Freidlin, Mark I.},
6313 file = {::},
6314 journal = {Trans. Amer. Math. Soc},
6315 number = {2},
6316 pages = {665--697},
6317 title = {{Random perturbations of reaction–diffusion equations: The quasi deterministic approximation}},
6318 url = {http://www.ams.org/tran/1988-305-02/S0002-9947-1988-0924775-7/S0002-9947-1988-0924775-7.pdf},
6319 volume = {305},
6320 year = {1988}
6321 }
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6323 author = {{De Masi}, A. and Ferrari, P. A. and Lebowitz, J. L.},
6324 file = {::},
6325 journal = {Physical review letters},
6326 number = {19},
6327 title = {{Rigorous derivation of reaction-diffusion equations with fluctuations}},
6328 url = {http://link.aps.org/doi/10.1103/PhysRevLett.55.1947},
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6330 year = {1985}
6331 }
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6333 author = {Aizenman, Michael},
6334 file = {::},
6335 journal = {Communications in Mathematical Physics},
6336 number = {1},
6337 pages = {1--48},
6338 publisher = {Springer},
6339 title = {{Geometric analysis of {$\varphi^4$} fields and Ising models. Parts I and II}},
6340 url = {http://www.springerlink.com/index/G3846K1Q6M79126N.pdf},
6341 volume = {86},
6342 year = {1982}
6343 }
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6346 doi = {10.1016/j.crma.2004.12.025},
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6348 issn = {1631073X},
6349 journal = {Comptes Rendus Mathematique},
6350 month = feb,
6351 number = {4},
6352 pages = {305--308},
6353 title = {{Invariant measures of stochastic partial differential equations and conditioned diffusions}},
6354 url = {http://linkinghub.elsevier.com/retrieve/pii/S1631073X0500021X},
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6356 year = {2005}
6357 }
6358 @article{Simon1977a,
6359 author = {Simon, Barry},
6360 file = {::},
6361 journal = {Advances in Mathematics},
6362 number = {3},
6363 pages = {244--273},
6364 publisher = {Elsevier},
6365 title = {{Notes on infinite determinants of Hilbert space operators}},
6366 url = {http://www.sciencedirect.com/science/article/pii/0001870877900573},
6367 volume = {24},
6368 year = {1977}
6369 }
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6371 author = {Feller, Willy},
6372 file = {::},
6373 journal = {Trans. Amer. Math. Soc},
6374 number = {488-515},
6375 pages = {102},
6376 title = {{On the integro-differential equations of purely discontinuous Markoff processes}},
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6378 volume = {48},
6379 year = {1940}
6380 }
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6383 doi = {10.1214/074921706000000239},
6384 file = {::},
6385 isbn = {0749217060000},
6386 journal = {Lecture Notes-Monograph Series},
6387 keywords = {-statistics,and,and phrases,berry-esseen,bootstrap,empirical,expansion,l-,r-,second order asymptotics,symmetric statistics},
6388 number = {2001},
6389 pages = {2--20},
6390 publisher = {JSTOR},
6391 title = {{From A to Z: Asymptotic expansions by van Zwet}},
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6393 volume = {36},
6394 year = {2001}
6395 }
6396 @article{fusco91,
6397 author = {Fusco, Giorgio and Rocha, Carlos},
6398 file = {::},
6399 journal = {Journal of differential equations},
6400 pages = {111--137},
6401 title = {{A permutation related to the dynamics of a scalar parabolic PDE}},
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6404 year = {1991}
6405 }
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6411 title = {{Asymptotic Eigenvalues of Sturm-Liouville Systems}},
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6415 @article{Funaki1992,
6416 author = {Funaki, Tadahisa},
6417 file = {::},
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6422 volume = {109},
6423 year = {1992}
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6427 doi = {10.1016/j.spl.2004.08.011},
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6429 issn = {01677152},
6430 journal = {Statistics \& Probability Letters},
6431 keywords = {diffusion process,equilibrium potential,last exit time,moment},
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6433 number = {2},
6434 pages = {155--169},
6435 title = {{The characterization of equilibrium potentials and last exit distributions for elliptic diffusion processes}},
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6442 doi = {10.1007/s10955-007-9351-8},
6443 file = {::},
6444 journal = {Journal of Statistical Physics},
6445 number = {5},
6446 pages = {1145--1152},
6447 publisher = {Springer},
6448 title = {{Anomalous dissipation in a stochastically forced infinite-dimensional system of coupled oscillators}},
6449 url = {http://www.springerlink.com/index/D42276761418P433.pdf},
6450 volume = {128},
6451 year = {2007}
6452 }
6453 @article{Hairer2009,
6454 author = {Hairer, Martin},
6455 file = {::},
6456 journal = {Arxiv preprint arXiv:0907.4178},
6457 title = {{An introduction to stochastic PDEs}},
6458 url = {http://arxiv.org/abs/0907.4178},
6459 year = {2009}
6460 }
6461 @article{Shardlow2003,
6462 author = {Shardlow, Tony},
6463 file = {::},
6464 journal = {BIT Numerical Mathematics},
6465 keywords = {initial-boundary value problems,partial differential equations,stochastic},
6466 number = {1},
6467 pages = {179--193},
6468 publisher = {Springer},
6469 title = {{Weak convergence of a numerical method for a stochastic heat equation}},
6470 url = {http://www.springerlink.com/index/X19H3682323XU0R6.pdf},
6471 volume = {43},
6472 year = {2003}
6473 }
6474 @article{Bott1982,
6475 author = {Bott, Raoul},
6476 doi = {10.1090/S0273-0979-1982-15038-8},
6477 file = {::},
6478 issn = {0273-0979},
6479 journal = {Bulletin of the American Mathematical Society},
6480 month = sep,
6481 number = {2},
6482 pages = {331--359},
6483 title = {{Lectures on Morse theory, old and new}},
6484 url = {http://www.ams.org/journal-getitem?pii=S0273-0979-1982-15038-8},
6485 volume = {7},
6486 year = {1982}
6487 }