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 @article{BBM10,
 author = {Barret, Florent and Bovier, Anton and M\'{e}l\'{e}ard, Sylvie},
 file = {::},
 journal = {Electronic Journal of Probability},
 pages = {323--345},
 publisher = {Institute of Mathematical Statistics},
 title = {{Uniform estimates for metastable transition times in a coupled bistable system}},
 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/viewarticle52a2.html?id=2066&layout=abstract},
 volume = {15},
 year = {2010}
 }
 @book{Dembo2009,
 author = {Dembo, A. and Zeitouni, O.},
 booktitle = {Media},
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 isbn = {9783642033100},
 publisher = {Springer Verlag},
 title = {{Large deviations techniques and applications}},
 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},
 volume = {38},
 year = {2009}
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 @article{gyongy.millet05,
 author = {Gy\"{o}ngy, Istv\'{a}n and Millet, Annie},
 file = {::},
 journal = {Potential Analysis},
 keywords = {coercivity,finite elements,monotone operators,stochastic evolution equations},
 number = {2},
 pages = {99--134},
 publisher = {Springer},
 title = {{On discretization schemes for stochastic evolution equations}},
 url = {http://www.springerlink.com/index/P8R487477340T18R.pdf},
 volume = {23},
 year = {2005}
 }
 @book{gilbarg.trudinger01,
 author = {Gilbarg, David and Trudinger, Neil S.},
 pages = {xiv+517},
 publisher = {Springer-Verlag},
 title = {{Elliptic partial differential equations of second order}},
 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},
 year = {2001}
 }
 @article{Winder2007,
 author = {Winder, Nick},
 file = {::},
 journal = {Ecology and Society},
 keywords = {adaptive potential,complex adaptive systems,cultural ecodynamics,innovation,metastability,resilience},
 number = {2},
 title = {{Innovation and metastability: A systems model}},
 url = {http://www.ibcperu.org/doc/isis/8159.pdf},
 volume = {12},
 year = {2007}
 }
 @article{daprato.debussche03,
 author = {{Da Prato}, Giuseppe and Debussche, Arnaud},
 file = {::},
 journal = {The Annals of Probability},
 number = {4},
 pages = {1900--1916},
 publisher = {Institute of Mathematical Statistics},
 title = {{Strong solutions to the stochastic quantization equations}},
 url = {http://projecteuclid.org/euclid.aop/1068646370},
 volume = {31},
 year = {2003}
 }
 @article{Anderssen1984,
 author = {Anderssen, RS},
 file = {::},
 journal = {BIT Numerical Mathematics},
 number = {January},
 pages = {401--412},
 title = {{On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions}},
 url = {http://www.springerlink.com/index/Q75534227QJ860V6.pdf},
 volume = {24},
 year = {1984}
 }
 @article{Berard1999,
 author = {Berard, A. and Grandati, Y.},
 file = {::},
 journal = {International journal of theoretical physics},
 number = {10},
 pages = {2535--2548},
 publisher = {Springer},
 title = {{Stochastic Quantization Approach for the Ising Model}},
 url = {http://www.springerlink.com/index/U184362764X571H6.pdf},
 volume = {38},
 year = {1999}
 }
 @article{Jiang1994,
 author = {Jiang, J.F.},
 file = {::},
 journal = {Journal of mathematical analysis and applications},
 number = {1},
 pages = {92--100},
 publisher = {Elsevier},
 title = {{Three-and four-dimensional cooperative systems with every equilibrium stable}},
 url = {http://www.sciencedirect.com/science/article/pii/S0022247X84714132},
 volume = {188},
 year = {1994}
 }
 @article{Funaki2004,
 author = {Funaki, Tadahisa},
 doi = {10.1214/009117904000000199},
 file = {::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 month = apr,
 number = {2},
 pages = {1201--1227},
 title = {{Zero temperature limit for interacting Brownian particles. I. Motion of a single body}},
 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884850/ http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884849/},
 volume = {32},
 year = {2004}
 }
 @incollection{bovier03,
 author = {Bovier, Anton},
 booktitle = {Lecture Notes TUB},
 file = {::},
 pages = {1--75},
 title = {{Markov processes and metastability}},
 url = {http://www-wt.iam.uni-bonn.de/$\sim$bovier/files/metavor.pdf},
 year = {2003}
 }
 @article{Mikami1990,
 author = {Mikami, T.},
 file = {::},
 journal = {The Annals of Probability},
 number = {2},
 pages = {524--536},
 publisher = {Institute of Mathematical Statistics},
 title = {{Asymptotic analysis of invariant density of randomly perturbed dynamical systems}},
 url = {http://projecteuclid.org/euclid.aop/1176990843},
 volume = {18},
 year = {1990}
 }
 @article{Mezard2001,
 archivePrefix = {arXiv},
 arxivId = {arXiv:cond-mat/0009418v1},
 author = {M\'{e}zard, Marc and Parisi, Giorgio},
 eprint = {0009418v1},
 file = {::},
 journal = {The European Physical Journal B-Condensed Matter and Complex Systems},
 number = {2},
 pages = {217--233},
 primaryClass = {arXiv:cond-mat},
 publisher = {Springer},
 title = {{The Bethe lattice spin glass revisited}},
 url = {http://www.springerlink.com/index/mg5p2ay9m48hlcw2.pdf},
 volume = {20},
 year = {2001}
 }
 @article{Dembo2005,
 author = {Dembo, A.},
 file = {::},
 journal = {Lectures on Probability Theory and Statistics},
 pages = {1--101},
 publisher = {Springer},
 title = {{Favorite points, cover times and fractals}},
 url = {http://www.springerlink.com/index/y7r377244560k334.pdf},
 volume = {1869},
 year = {2005}
 }
 @article{VdEW08,
 author = {Vanden-Eijnden, Eric and Westdickenberg, Maria G.},
 doi = {10.1007/s10955-008-9537-8},
 file = {::},
 isbn = {1095500895378},
 issn = {0022-4715},
 journal = {Journal of Statistical Physics},
 keywords = {large deviation theory,metastability,nucleation,phase transformation,rare events,small noise,spatially extended system,stochastic partial differential equation},
 month = apr,
 number = {6},
 pages = {1023--1038},
 title = {{{Rare Events in Sto\-chas\-tic Partial Differential Equations on Large Spatial Domains}}},
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 volume = {131},
 year = {2008}
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 author = {Chapuy, Guillaume},
 doi = {10.1017/S0000000000000000},
 file = {::},
 isbn = {0000000000000},
 journal = {Combinatorics, Probability and Computing},
 keywords = {algebraic series,asymptotic combinatorics,bijec-,graphs on surfaces},
 number = {04},
 pages = {477--516},
 publisher = {Cambridge Univ Press},
 title = {{Asymptotic enumeration of constellations and related families of maps on orientable surfaces}},
 url = {http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=5794560},
 volume = {18},
 year = {2009}
 }
 @article{Bak2002,
 author = {Bak, JG and Shkalikov, A. A.},
 file = {::},
 journal = {Mathematical Notes},
 keywords = {distribution potentials,multipliers,schr,sobolev spaces},
 number = {5},
 pages = {587--594},
 publisher = {Springer},
 title = {{Multipliers in Dual Sobolev Spaces and Schr\"{o}dinger Operators with Distribution Potentials}},
 url = {http://www.springerlink.com/index/E7J8GP8W5EVNGQ2H.pdf},
 volume = {71},
 year = {2002}
 }
 @article{Kalton2007,
 author = {Kalton, NJ and Mayboroda, Svitlana and Mitrea, Marius},
 file = {::},
 journal = {Contemporary Mathematics},
 pages = {121},
 publisher = {Providence, RI; American Mathematical Society; 1999},
 title = {{Interpolation of Hardy-Sobolev-Besov-Triebel-Lizorkin spaces and applications to problems in partial differential equations}},
 url = {http://www.math.purdue.edu/$\sim$svitlana/milman_conf.pdf},
 volume = {445},
 year = {2007}
 }
 @misc{Malrieu2006,
 author = {Malrieu, F.},
 booktitle = {perso.univ-rennes1.fr},
 file = {::},
 title = {{Processus de Markov et in\'{e}galit\'{e}s fonctionnelles}},
 url = {http://perso.univ-rennes1.fr/florent.malrieu/MASTER2/markov180406.pdf},
 year = {2006}
 }
 @article{Mugnai2007a,
 archivePrefix = {arXiv},
 arxivId = {arXiv:0704.1954v2},
 author = {Mugnai, Luca and R\"{o}ger, Matthias},
 eprint = {arXiv:0704.1954v2},
 file = {::},
 journal = {Arxiv preprint arXiv:0704.1954},
 pages = {1--33},
 title = {{The Allen-Cahn action functional in higher dimensions}},
 url = {http://arxiv.org/abs/0704.1954},
 volume = {1},
 year = {2007}
 }
 @article{Herrmann2008,
 author = {Herrmann, Samuel and Imkeller, Peter and Peithmann, Dierk},
 doi = {10.1214/07-AAP489},
 file = {::},
 issn = {1050-5164},
 journal = {The Annals of Applied Probability},
 month = aug,
 number = {4},
 pages = {1379--1423},
 title = {{Large deviations and a Kramers’ type law for self-stabilizing diffusions}},
 url = {http://projecteuclid.org/euclid.aoap/1216677126},
 volume = {18},
 year = {2008}
 }
 @article{Morosi2010,
 archivePrefix = {arXiv},
 arxivId = {arXiv:0902.0708v1},
 author = {Morosi, Carlo and Pizzocchero, Livio},
 eprint = {arXiv:0902.0708v1},
 file = {::},
 journal = {Advances in Applied Mathematics},
 keywords = {26d10,46e35,47a60,ams 2000 subject classifications,inequalities,pointwise multiplication,sobolev spaces},
 number = {4},
 pages = {393--432},
 publisher = {Elsevier},
 title = {{New results on multiplication in Sobolev spaces}},
 url = {http://www.sciencedirect.com/science/article/pii/S0196885809001250},
 volume = {44},
 year = {2010}
 }
 @inproceedings{Voros1993,
 author = {Voros, A.},
 booktitle = {Annales de l'institut Fourier},
 file = {::},
 number = {5},
 pages = {1509--1534},
 publisher = {Chartres: L'Institut, 1950-},
 title = {{R\'{e}surgence quantique}},
 url = {http://archive.numdam.org/article/AIF_1993__43_5_1509_0.pdf},
 volume = {43},
 year = {1993}
 }
 @article{Yoo2000,
 author = {Yoo, Hyek},
 file = {::},
 journal = {Mathematics of Computation},
 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},
 number = {230},
 pages = {653--666},
 title = {{Semi-discretization of stochastic partial differential equations on R1 by a finite-difference method}},
 url = {http://www.ams.org/mcom/2000-69-230/S0025-5718-99-01150-3/S0025-5718-99-01150-3.pdf},
 volume = {69},
 year = {2000}
 }
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 journal = {Communications on pure and applied mathematics},
 number = {12},
 pages = {1627--1672},
 publisher = {Wiley Online Library},
 title = {{Gamma-convergence of gradient flows with applications to Ginzburg-Landau}},
 url = {http://onlinelibrary.wiley.com/doi/10.1002/cpa.20046/abstract},
 volume = {57},
 year = {2004}
 }
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 issn = {0178-8051},
 journal = {Probability Theory and Related Fields},
 keywords = {2000,60h15,60j45,hitting probabilities,malliavin calculus,mathematics subject classification,noise,primary,secondary,space-time white,stochastic heat equation},
 month = apr,
 number = {3-4},
 pages = {371--427},
 title = {{Hitting probabilities for systems of non-linear stochastic heat equations with multiplicative noise}},
 url = {http://www.springerlink.com/index/10.1007/s00440-008-0150-1},
 volume = {144},
 year = {2008}
 }
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 journal = {Proceedings of the American Mathematical Society},
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 pages = {3027--3038},
 publisher = {Providence, RI [etc.] American Mathematical Society.},
 title = {{On the determinant of elliptic boundary value problems on a line segment}},
 url = {http://www.ams.org/journals/proc/1995-123-10/S0002-9939-1995-1301012-4/S0002-9939-1995-1301012-4.pdf},
 volume = {123},
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 journal = {Annals of probability},
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 publisher = {JSTOR},
 title = {{Brownian sheet and capacity}},
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 year = {1999}
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 @article{Fix1967b,
 author = {Fix, George},
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 journal = {Journal of Mathematical Analysis and Applications},
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 volume = {19},
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 @article{Glover1982,
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 journal = {Annales scientifiques de l'Universit\'{e} de Clermont-Ferrand},
 pages = {107},
 title = {{Markov processes and their last exit distributions}},
 volume = {71},
 year = {1982}
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 @article{Majda2003,
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 file = {::},
 journal = {Journal of the Atmospheric Sciences},
 number = {14},
 pages = {1705--1722},
 title = {{Systematic strategies for stochastic mode reduction in climate}},
 url = {http://journals.ametsoc.org/doi/pdf/10.1175/1520-0469(2003)060%3C1705%3ASSFSMR%3E2.0.CO%3B2},
 volume = {60},
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 @article{Allen2003,
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 journal = {Theoretical Population Biology},
 keywords = {birth and death process,logistic equation,markov chain,persistence time,stochastic differential equation},
 month = dec,
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 pages = {439--449},
 title = {{A comparison of three different stochastic population models with regard to persistence time}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0040580903001047},
 volume = {64},
 year = {2003}
 }
 @article{Hairer2007b,
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 issn = {1050-5164},
 journal = {The Annals of Applied Probability},
 month = oct,
 number = {5/6},
 pages = {1657--1706},
 title = {{Analysis of SPDEs arising in path sampling part II: The nonlinear case}},
 url = {http://projecteuclid.org/euclid.aoap/1191419180},
 volume = {17},
 year = {2007}
 }
 @article{BEGK00,
 archivePrefix = {arXiv},
 arxivId = {arXiv:cond-mat/0007343v1},
 author = {Bovier, Anton and Eckhoff, Michael and Gayrard, V\'{e}ronique and Klein, Markus},
 eprint = {0007343v1},
 file = {::},
 journal = {Journal of Physics A: Mathematical and General},
 keywords = {eigenvalue problems,exponential distribution,markov chains,metastability},
 pages = {L447},
 primaryClass = {arXiv:cond-mat},
 publisher = {IOP Publishing},
 title = {{Metastability and small eigenvalues in Markov chains}},
 url = {http://iopscience.iop.org/0305-4470/33/46/102},
 volume = {33},
 year = {2000}
 }
 @book{chung.walsh05,
 author = {Chung, Kai Lai and Walsh, John B.},
 pages = {xii+431},
 publisher = {Springer-Verlag},
 title = {{Markov processes, {B}rownian motion, and time symmetry}},
 year = {2005}
 }
 @article{Maas2011,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1102.5238v1},
 author = {Maas, Jan},
 eprint = {arXiv:1102.5238v1},
 file = {::},
 journal = {Journal of Functional Analysis},
 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},
 pages = {1--32},
 publisher = {Elsevier},
 title = {{Gradient flows of the entropy for finite Markov chains}},
 url = {http://www.sciencedirect.com/science/article/pii/S0022123611002278},
 year = {2011}
 }
 @book{courant.hilbert1,
 author = {Courant, R. and Hilbert, D.},
 publisher = {Interscience Publishers},
 title = {{Methods of mathematical physics. {V}ol. {I}}},
 year = {1953}
 }
 @article{Westdickenberg2007,
 author = {Westdickenberg, Maria G. and Tonegawa, Yoshihiro},
 file = {::},
 journal = {Indiana University Mathematics Journal},
 number = {6},
 title = {{Higher multiplicity in the one-dimensional Allen-Cahn action functional}},
 url = {http://eprints3.math.sci.hokudai.ac.jp/1660/1/pre821.pdf},
 volume = {56},
 year = {2007}
 }
 @article{Iwata1987,
 author = {Iwata, K.},
 file = {::},
 journal = {Probability theory and related fields},
 number = {1},
 pages = {141--159},
 publisher = {Springer},
 title = {{An infinite dimensional stochastic differential equation with state space C(R)}},
 url = {http://www.springerlink.com/index/G31PM6220370N4X7.pdf},
 volume = {74},
 year = {1987}
 }
 @article{Eckmann2003,
 author = {Eckmann, J.-P. and Hairer, M.},
 doi = {10.1007/s00220-003-0805-9},
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 issn = {0010-3616},
 journal = {Communications in Mathematical Physics},
 month = apr,
 number = {2},
 pages = {233--253},
 title = {{Spectral Properties of Hypoelliptic Operators}},
 url = {http://www.springerlink.com/Index/10.1007/s00220-003-0805-9},
 volume = {235},
 year = {2003}
 }
 @article{Fulton1994,
 author = {Fulton, Charles T. and Pruess, Steven A.},
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 journal = {Journal of Mathematical Analysis and Applications},
 pages = {297--340},
 title = {{Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems}},
 url = {http://www.sciencedirect.com/science/article/pii/S0022247X84714296},
 volume = {188},
 year = {1994}
 }
 @article{Bobrovsky1992,
 author = {Bobrovsky, B.Z. and Zeitouni, O.},
 file = {::},
 journal = {Stochastic processes and their applications},
 number = {2},
 pages = {241--256},
 publisher = {Elsevier},
 title = {{Some results on the problem of exit from a domain}},
 url = {http://www.sciencedirect.com/science/article/pii/0304414992901249},
 volume = {41},
 year = {1992}
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 @article{Gyongy2009,
 author = {Gy\"{o}ngy, Istv\'{a}n and Krylov, NV},
 file = {::},
 journal = {Math. Comp},
 keywords = {and phrases,cauchy problem,finite differences,first derivatives estimates},
 number = {268},
 pages = {2019--2046},
 title = {{First derivatives estimates for finite-difference schemes}},
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 volume = {78},
 year = {2009}
 }
 @article{Fiedler2008,
 author = {Fiedler, Bernold and Rocha, Carlos},
 doi = {10.1016/j.jde.2007.09.015},
 file = {::},
 issn = {00220396},
 journal = {Journal of Differential Equations},
 month = mar,
 number = {5},
 pages = {1255--1286},
 title = {{Connectivity and design of planar global attractors of Sturm type. II: Connection graphs}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039607003026},
 volume = {244},
 year = {2008}
 }
 @article{freidlin85,
 author = {Freidlin, M},
 file = {::},
 journal = {The Annals of Probability},
 number = {3},
 pages = {639--675},
 title = {{Limit theorems for large deviations and reaction-diffusion equations}},
 url = {http://www.jstor.org/stable/10.2307/2243706},
 volume = {13},
 year = {1985}
 }
 @article{Mugnai2007,
 author = {Mugnai, L. and R\"{o}ger, M.},
 file = {::},
 journal = {Arxiv preprint arXiv:0704.1954},
 keywords = {allen,cahn equation,large deviation theory,motion by mean curvature,sharp interface limits,stochastic partial differential equations},
 pages = {45--78},
 title = {{The Allen-Cahn action functional in higher dimensions}},
 url = {http://arxiv.org/abs/0704.1954},
 volume = {10},
 year = {2007}
 }
 @article{LLLP11,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1105.4636v1},
 author = {{Le Bris}, Claude and Leli\`{e}vre, Tony and Luskin, M. and Perez, D.},
 eprint = {arXiv:1105.4636v1},
 file = {::},
 journal = {preprint arXiv:1105.4636},
 number = {1},
 pages = {1--21},
 title = {{A mathematical formalization of the parallel replica dynamics}},
 url = {http://arxiv.org/abs/1105.4636},
 year = {2011}
 }
 @article{Chen1987,
 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.},
 author = {Chen, Y D},
 file = {::},
 issn = {0027-8424},
 journal = {Proceedings of the National Academy of Sciences of the United States of America},
 keywords = {Biological Transport,Kinetics,Mathematics,Membrane Potentials,Models, Biological,Thermodynamics},
 month = feb,
 number = {3},
 pages = {729--33},
 pmid = {3468510},
 title = {{Asymmetry and external noise-induced free energy transduction.}},
 url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=304289&tool=pmcentrez&rendertype=abstract},
 volume = {84},
 year = {1987}
 }
 @article{Rougemont2002,
 author = {Rougemont, Jacques},
 file = {::},
 journal = {Communications in mathematical physics},
 number = {2},
 pages = {423--448},
 publisher = {Springer},
 title = {{Space-time invariant measures, entropy, and dimension for stochastic Ginzburg–Landau equations}},
 url = {http://www.springerlink.com/index/yl83egjhcarxdy2v.pdf},
 volume = {225},
 year = {2002}
 }
 @book{Hubbell2001,
 author = {Hubbell, SP},
 booktitle = {Monographs in Population Biology},
 file = {::},
 isbn = {0691021295},
 title = {{The unified neutral theory of biodiversity and biogeography}},
 url = {http://books.google.com/books?hl=en&lr=&id=EIQpFBu84NoC&oi=fnd&pg=PR3&dq=the+unified+neutral+theory+of+Biodiversity+and+Biogeography&ots=cPHWIZKzt-&sig=LZzxdQAOYuY4W_B_WJi458D9P10},
 year = {2001}
 }
 @article{Kalies2000,
 author = {Kalies, WD and Kwapisz, J and van den Berg, J. B.},
 file = {::},
 journal = {Communications in},
 number = {November 2000},
 pages = {573--592},
 title = {{Homotopy Classes for Stable Periodic and Chaotic\P Patterns in Fourth-Order Hamiltonian Systems}},
 url = {http://www.springerlink.com/index/2QD9TJWJJP3XMJ5C.pdf},
 volume = {707},
 year = {2000}
 }
 @article{Lesch1998,
 author = {Lesch, Matthias and Tolksdorf, J\"{u}rgen},
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 author = {Cahn, John W. and Hilliard, John E.},
 doi = {10.1063/1.1744102},
 file = {::},
 issn = {00219606},
 journal = {The Journal of Chemical Physics},
 number = {2},
 pages = {258},
 title = {{Free Energy of a Nonuniform System. I. Interfacial Free Energy}},
 url = {http://link.aip.org/link/JCPSA6/v28/i2/p258/s1&Agg=doi},
 volume = {28},
 year = {1958}
 }
 @article{levin98,
 author = {Levin, S.A.},
 file = {::},
 journal = {Ecosystems},
 keywords = {complex adap-,functional group,gaia,homeostasis,keystone,nonlinearity,self-organization,species,tive system},
 number = {5},
 pages = {431--436},
 publisher = {Springer},
 title = {{Ecosystems and the biosphere as complex adaptive systems}},
 url = {http://www.springerlink.com/index/VKNT5TK0BCPFC7X1.pdf},
 volume = {1},
 year = {1998}
 }
 @article{Berglund2001,
 archivePrefix = {arXiv},
 arxivId = {arXiv:math/0111178v1},
 author = {Berglund, Nils},
 eprint = {0111178v1},
 file = {::;::},
 journal = {Arxiv preprint math/0111178},
 primaryClass = {arXiv:math},
 title = {{Perturbation theory of dynamical systems}},
 url = {http://arxiv.org/abs/math/0111178},
 year = {2001}
 }
 @article{Funaki2006,
 author = {Funaki, Tadahisa and Kikuchi, Masashi and Potthoff, J\"{u}rgen},
 file = {::},
 journal = {Preprint},
 keywords = {60g17,60g60,60h15,ams subject classification,direction-dependent modulus of continuity,dom fields,garsia-rodemich-rumsey lemma,kolmogorov- centsov,ran-,sample continuity,theorem},
 pages = {1--13},
 title = {{Direction-dependent modulus of continuity for random fields}},
 url = {http://www.ms.u-tokyo.ac.jp/$\sim$funaki/publ/Fu-Ki-Pott.pdf},
 year = {2006}
 }
 @article{Kohn2006,
 author = {Kohn, Robert V. and Reznikoff, Maria G. and Tonegawa, Yoshihiro},
 doi = {10.1007/s00526-005-0370-5},
 file = {::},
 issn = {0944-2669},
 journal = {Calculus of Variations and Partial Differential Equations},
 keywords = {action minimization,allen-cahn equation,gamma,large deviation theory,sharp-interface limits,stochastic partial differential equations},
 month = feb,
 number = {4},
 pages = {503--534},
 title = {{Sharp-interface limit of the Allen-Cahn action functional in one space dimension}},
 url = {http://www.springerlink.com/index/10.1007/s00526-005-0370-5},
 volume = {25},
 year = {2006}
 }
 @article{Faierman1972,
 author = {Faierman, M.},
 file = {::},
 journal = {Journal of Differential Equations},
 pages = {10--37},
 title = {{An oscillation theorem for a one-parameter ordinary differential equation of the second order}},
 url = {http://adsabs.harvard.edu/abs/1972JDE....11...10F},
 volume = {11},
 year = {1972}
 }
 @article{Getoor1986,
 author = {Getoor, R. K. and Steffens, J.},
 file = {::},
 journal = {Probability theory and related fields},
 pages = {415--445},
 title = {{Capacity theory without duality}},
 url = {http://www.springerlink.com/index/P2JVQ45X61274830.pdf},
 volume = {73},
 year = {1986}
 }
 @article{Allman2009,
 author = {Allman, Michael and Betz, Volker},
 doi = {10.1016/j.spa.2009.01.007},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 keywords = {asymptotic theory,first-exit from space,interacting brownian particles,time domains},
 month = aug,
 number = {8},
 pages = {2645--2659},
 publisher = {Elsevier B.V.},
 title = {{Breaking the chain}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414909000283},
 volume = {119},
 year = {2009}
 }
 @article{gyongy.pardoux93a,
 author = {Gy\"{o}ngy, Istv\'{a}n and Pardoux, Etienne},
 file = {::},
 journal = {Probability theory and related fields},
 pages = {211--229},
 title = {{On the regularization effect of space-time white noise on quasi-linear parabolic partial differential equations}},
 url = {http://www.springerlink.com/index/j7523u2h87384792.pdf},
 volume = {97},
 year = {1993}
 }
 @article{fiedler.rocha10,
 author = {Fiedler, Bernold and Rocha, Carlos},
 doi = {10.1515/CRELLE.2009.076},
 file = {::},
 journal = {Journal of Dynamics and Differential Equations},
 number = {2},
 pages = {121--162},
 publisher = {Springer},
 title = {{Connectivity and design of planar global attractors of Sturm type. III: Small and Platonic examples}},
 url = {http://www.springerlink.com/index/e1867pl607792418.pdf},
 volume = {22},
 year = {2010}
 }
 @article{Fukushima2004,
 author = {Fukushima, Masatoshi and He, Ping and Ying, Jiangang},
 doi = {10.1214/009117904000000649},
 file = {::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 month = oct,
 number = {4},
 pages = {3138--3166},
 title = {{Time changes of symmetric diffusions and Feller measures}},
 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1107883349/},
 volume = {32},
 year = {2004}
 }
 @article{El-Gendi1969,
 author = {El-Gendi, SE},
 file = {::},
 journal = {The Computer Journal},
 number = {3},
 pages = {282--287},
 publisher = {Br Computer Soc},
 title = {{Chebyshev solution of differential, integral and integro-differential equations}},
 url = {http://comjnl.oxfordjournals.org/content/12/3/282.short},
 volume = {12},
 year = {1969}
 }
 @book{kunita,
 author = {Kunita, Hiroshi},
 edition = {{re\-print}},
 pages = {xiv+346},
 publisher = {Cambridge University Press},
 title = {{Stochastic flows and stochastic differential equations}},
 year = {1997}
 }
 @article{eckhoff05,
 author = {Eckhoff, Michael},
 doi = {10.1214/009117904000000991},
 file = {::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 month = jan,
 number = {1},
 pages = {244--299},
 title = {{Precise asymptotics of small eigenvalues of reversible diffusions in the metastable regime}},
 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1108141727/},
 volume = {33},
 year = {2005}
 }
 @article{Reddien1976,
 author = {Reddien, GW},
 file = {::},
 journal = {Math. Comp},
 number = {134},
 pages = {278--282},
 title = {{Finite-Difference Approximation to Singular Sturm-Liouville Eigenvalue Problems}},
 url = {http://www.ams.org/journals/mcom/1976-30-134/S0025-5718-1976-0403235-1/S0025-5718-1976-0403235-1.pdf},
 volume = {30},
 year = {1976}
 }
 @article{Barnett1925,
 author = {Barnett, IA},
 file = {::},
 journal = {Bull. Amer. Math. Soc},
 pages = {263--265},
 title = {{Integro-differential equations}},
 url = {http://www.ams.org/bull/1925-31-05/S0002-9904-1925-04048-3/S0002-9904-1925-04048-3.pdf},
 year = {1925}
 }
 @article{Lesch1998a,
 archivePrefix = {arXiv},
 arxivId = {arXiv:math/9902114v1},
 author = {Lesch, Matthias},
 eprint = {9902114v1},
 file = {::},
 journal = {Mathematische Nachrichten},
 keywords = {and phrases,determinants,liouville theory,sturm},
 number = {1},
 pages = {139--170},
 primaryClass = {arXiv:math},
 publisher = {Wiley Online Library},
 title = {{Determinants of Regular Singular Sturm-Liouville Operators}},
 url = {http://onlinelibrary.wiley.com/doi/10.1002/mana.19981940110/abstract},
 volume = {194},
 year = {1998}
 }
 @article{Gyongy1998,
 author = {Gy\"{o}ngy, Istv\'{a}n},
 file = {::},
 journal = {Stochastic Processes and their Applications},
 pages = {271--299},
 title = {{Existence and uniqueness results for semilinear stochastic partial differential equations}},
 url = {http://www.sciencedirect.com/science/article/pii/S0304414997001038},
 volume = {73},
 year = {1998}
 }
 @article{meleard.villemonais11,
 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.},
 archivePrefix = {arXiv},
 arxivId = {1112.4732},
 author = {M\'{e}l\'{e}ard, Sylvie and Villemonais, Denis},
 eprint = {1112.4732},
 month = dec,
 title = {{Quasi-stationary distributions and population processes}},
 url = {http://arxiv.org/abs/1112.4732},
 year = {2011}
 }
 @article{MOS90,
 author = {Martinelli, Fabio and Olivieri, Enzo and Scoppola, Elisabetta},
 file = {::},
 journal = {Journal of statistical physics},
 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},
 number = {5},
 pages = {1105--1119},
 publisher = {Springer},
 title = {{Metastability and exponential approach to equilibrium for low-temperature stochastic Ising models}},
 url = {http://www.springerlink.com/index/u43216617w08xh17.pdf},
 volume = {61},
 year = {1990}
 }
 @article{eyring35,
 author = {Eyring, H},
 file = {::},
 journal = {The Journal of Chemical Physics},
 title = {{The activated complex in chemical reactions}},
 url = {http://link.aip.org/link/?jcp/3/107},
 volume = {3},
 year = {1935}
 }
 @techreport{Bovier2009,
 author = {Bovier, Anton},
 booktitle = {Spin Glasses: Statics and Dynamics},
 file = {::},
 pages = {40},
 publisher = {Springer},
 title = {{A Short Course on Mean Field Spin Glasses}},
 url = {http://www.springerlink.com/index/R571857J605253X0.pdf},
 year = {2009}
 }
 @article{Theory2009,
 author = {Camilli, Fabio and Cesaroni, Annalisa},
 file = {::},
 journal = {Journal of Dynamical Systems},
 keywords = {and phrases,large deviations,pde aubry-mather theory,random perturbations of dynamical,systems,tions,viscosity solu-},
 pages = {1--28},
 title = {{Randomly perturbed dynamical systems and Aubry-Mather theory}},
 url = {http://inderscience.metapress.com/index/e145361275746ku6.pdf},
 year = {2009}
 }
 @article{bouchaud.mezard97,
 author = {Bouchaud, J.P. and M\'{e}zard, Marc},
 file = {::},
 journal = {Physica D: Nonlinear Phenomena},
 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},
 number = {2-4},
 pages = {174--182},
 publisher = {Elsevier},
 title = {{Landscape approach for pinned elastic interfaces}},
 url = {http://www.sciencedirect.com/science/article/pii/S0167278997000845},
 volume = {107},
 year = {1997}
 }
 @article{Debussche2009,
 author = {Debussche, Arnaud and Printems, Jacques},
 file = {::},
 journal = {Math. Comp},
 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},
 number = {266},
 pages = {845--863},
 title = {{Weak order for the discretization of the stochastic heat equation}},
 url = {http://www.ams.org/mcom/2009-78-266/S0025-5718-08-02184-4/S0025-5718-08-02184-4.pdf},
 volume = {78},
 year = {2009}
 }
 @article{barret12,
 author = {Barret, Florent},
 institution = {CMAP},
 journal = {pr\'{e}publication CMAP, soumis.},
 title = {{Sharp asymptotics of metastable transition times for one dimensional SPDEs}},
 year = {2012}
 }
 @article{wolfrum02,
 author = {Wolfrum, Matthias},
 doi = {10.1006/jdeq.2001.4114},
 file = {::},
 issn = {00220396},
 journal = {Journal of Differential Equations},
 keywords = {attractors,heteroclinic connections,nodal properties,order structures,scalar semilinear parabolic pde},
 month = jul,
 number = {1},
 pages = {56--78},
 title = {{A Sequence of Order Relations: Encoding Heteroclinic Connections in Scalar Parabolic PDE}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039601941142},
 volume = {183},
 year = {2002}
 }
 @article{IP08,
 author = {Imkeller, Peter and Pavlyukevich, Ilya},
 doi = {10.1051/ps},
 file = {::},
 journal = {{\\ ESAIM: Probability and Statistics}},
 keywords = {and phrases,evy process,extreme events,first exit time,heavy tail,jump diffusion,l,metastability,regular variation},
 number = {July},
 pages = {412--437},
 title = {{Metastable Behaviour of Small Noise Levy-Driven Diffusion}},
 url = {http://cdsweb.cern.ch/record/926151},
 volume = {12},
 year = {2008}
 }
 @book{Cerrai2001,
 author = {Cerrai, Sandra},
 booktitle = {Lecture Notes in Mathematics},
 file = {::},
 isbn = {354042136X},
 pages = {329},
 title = {{Second order PDEs in finite and infinite dimension}},
 year = {2001}
 }
 @article{DaPrato1996,
 author = {{Da Prato}, Giuseppe and Debussche, Arnaud},
 file = {::},
 journal = {Nonlinear Analysis: Theory, Methods \& Applications},
 keywords = {and phrases,stochastic equations,white noise},
 number = {2},
 pages = {241--263},
 title = {{Stochastic Cahn-Hilliard equation}},
 url = {http://www.newton.ac.uk/programmes/SPD/seminars/063010101.pdf},
 volume = {26},
 year = {1996}
 }
 @article{KKR93,
 author = {Kavian, Otared and Kerkyacharian, G\'{e}rard and Roynette, Bernard},
 file = {::},
 journal = {Journal of functional analysis},
 pages = {155--196},
 title = {{Quelques remarques sur l'ultracontractivit\'{e}}},
 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=4642605},
 volume = {111},
 year = {1993}
 }
 @article{BFG07b,
 archivePrefix = {arXiv},
 arxivId = {arXiv:math/0611648v2},
 author = {Berglund, Nils and Fernandez, Bastien and Gentz, Barbara},
 eprint = {0611648v2},
 file = {::},
 journal = {Nonlinearity},
 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},
 pages = {2583},
 primaryClass = {arXiv:math},
 publisher = {IOP Publishing},
 title = {{Metastability in interacting nonlinear stochastic differential equations: II. Large-N behaviour}},
 url = {http://iopscience.iop.org/0951-7715/20/11/006 http://iopscience.iop.org/0951-7715/20/11/007},
 volume = {20},
 year = {2007}
 }
 @article{Kuttler1970,
 author = {Kuttler, J.R.},
 file = {::},
 journal = {SIAM Journal on Numerical Analysis},
 number = {2},
 pages = {206--232},
 publisher = {JSTOR},
 title = {{Finite difference approximations for eigenvalues of uniformly elliptic operators}},
 url = {http://www.jstor.org/stable/10.2307/2949456},
 volume = {7},
 year = {1970}
 }
 @article{Gyongy2001,
 author = {Gy\"{o}ngy, Istv\'{a}n and Martinez, Teresa},
 file = {::},
 journal = {Czechoslovak Mathematical Journal},
 keywords = {krylov,s estimate,stochastic differential equations},
 number = {4},
 pages = {763--783},
 publisher = {Springer},
 title = {{On stochastic differential equations with locally unbounded drift}},
 url = {http://www.springerlink.com/index/HG25TU50XWHJ1775.pdf},
 volume = {51},
 year = {2001}
 }
 @incollection{Holden2010,
 author = {Holden, Helge and Oksendal, Bernt and Uboe, Jan and Zhang, Tusheng},
 booktitle = {Stochastic partial differential equations},
 file = {::},
 title = {{Stochastic partial differential equations, frontmatter}},
 url = {http://www.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=A8325264AH},
 year = {2010}
 }
 @article{Adams2010,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1004.4076v1},
 author = {Adams, Stefan and Dirr, Nicolas and Peletier, M.A. and Zimmer, Johannes},
 eprint = {arXiv:1004.4076v1},
 file = {::},
 journal = {Communications in Mathematical Physics},
 keywords = {and phrases,gamma-convergence,generalized gradient flows,hydrodynamic limits,optimal transport,stochastic particle systems,tional evolution equations,varia-},
 number = {2},
 pages = {1--25},
 publisher = {Springer},
 title = {{From a large-deviations principle to the Wasserstein gradient flow: A new micro-macro passage}},
 url = {http://www.springerlink.com/index/C5176KX3T224N276.pdf},
 year = {2010}
 }
 @article{HKN04,
 author = {Helffer, Bernard and Klein, Markus and Nier, Francis},
 journal = {Mat. Contemp.},
 pages = {41--85},
 title = {{Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach}},
 url = {http://hal.archives-ouvertes.fr/inria-00001236/},
 volume = {26},
 year = {2004}
 }
 @article{Dreyfus1978,
 author = {Dreyfus, Tommy and Dym, Harry},
 file = {::},
 journal = {Duke Mathematical Journal},
 number = {1},
 title = {{Product formulas for the eigenvalues of a class of boundary value problems}},
 url = {http://projecteuclid.org/euclid.dmj/1077312684},
 volume = {45},
 year = {1978}
 }
 @article{Desvillettes2004,
 author = {Desvillettes, L. and Villani, C.},
 doi = {10.1007/s00222-004-0389-9},
 file = {::},
 issn = {0020-9910},
 journal = {Inventiones mathematicae},
 month = sep,
 number = {2},
 pages = {245--316},
 title = {{On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation}},
 url = {http://www.springerlink.com/index/10.1007/s00222-004-0389-9},
 volume = {159},
 year = {2004}
 }
 @article{Parter1982,
 author = {Parter, SV},
 file = {::},
 journal = {SIAM Journal on Numerical Analysis},
 number = {3},
 pages = {518--530},
 title = {{On the eigenvalues of second order elliptic difference operators}},
 url = {http://www.jstor.org/stable/10.2307/2156965},
 volume = {19},
 year = {1982}
 }
 @article{BGW11,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1109.0449v1},
 author = {Bodineau, Thierry and Graham, Benjamin and Wouts, Marc},
 eprint = {arXiv:1109.0449v1},
 file = {::},
 journal = {Arxiv preprint arXiv:1109.0449},
 title = {{Metastability in the dilute Ising model}},
 url = {http://arxiv.org/abs/1109.0449},
 year = {2011}
 }
 @article{CGOV84,
 author = {Cassandro, Marzio and Galves, A. and Olivieri, Enzo and Vares, M.E.},
 file = {::},
 journal = {Journal of statistical physics},
 number = {5},
 pages = {603--634},
 publisher = {Springer},
 title = {{Metastable behavior of stochastic dynamics: a pathwise approach}},
 url = {http://www.springerlink.com/index/LJ15242528467W34.pdf},
 volume = {35},
 year = {1984}
 }
 @article{BdHS10,
 author = {Bovier, Anton and den Hollander, Frank and Spitoni, Cristian},
 doi = {10.1214/09-AOP492},
 file = {::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 keywords = {and phrases,berman,capacity,critical droplet,dirichlet principle,glauber dynamics,kawasaki dynamics,konsowa principle,last-exit biased distribution,metastable tran-,sition time},
 month = mar,
 number = {2},
 pages = {661--713},
 title = {{Homogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures}},
 url = {http://projecteuclid.org/euclid.aop/1268143530},
 volume = {38},
 year = {2010}
 }
 @article{Funaki1989,
 author = {Funaki, Tadahisa},
 file = {::},
 journal = {Probability Theory and Related Fields},
 pages = {39--93},
 title = {{Derivation of the hydrodynamical equation for one-dimensional Ginzburg-Landau model}},
 url = {http://www.springerlink.com/index/V50502526002212L.pdf},
 volume = {82},
 year = {1989}
 }
 @article{Khoshnevisan2008,
 author = {Khoshnevisan, Davar and Levin, D. and Mendezhernandez, P.},
 doi = {10.1016/j.spa.2007.10.014},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 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},
 month = oct,
 number = {10},
 pages = {1723--1737},
 title = {{Capacities in Wiener space, quasi-sure lower functions, and Kolmogorov’s $\epsilon$$\epsilon$-entropy}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414907001998},
 volume = {118},
 year = {2008}
 }
 @article{Bansaye2009,
 author = {Bansaye, Vincent},
 doi = {10.1016/j.spa.2008.12.005},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 keywords = {bpre,branching process in random,environment,q-process,random walk with,yaglom distribution},
 month = aug,
 number = {8},
 pages = {2436--2464},
 publisher = {Elsevier B.V.},
 title = {{Surviving particles for subcritical branching processes in random environment}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908001890},
 volume = {119},
 year = {2009}
 }
 @article{Coskun2005,
 author = {Coşkun, Haskız and Bayram, Neslihan},
 doi = {10.1016/j.jmaa.2004.10.030},
 file = {::},
 issn = {0022247X},
 journal = {Journal of Mathematical Analysis and Applications},
 keywords = {asymptotics,eigenparameter,eigenvalues,liouville problems,sturm},
 month = jun,
 number = {2},
 pages = {548--566},
 title = {{Asymptotics of eigenvalues for regular Sturm–Liouville problems with eigenvalue parameter in the boundary condition}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022247X04008698},
 volume = {306},
 year = {2005}
 }
 @article{Seeley1969,
 author = {Seeley, R},
 file = {::},
 journal = {American Journal of Mathematics},
 number = {4},
 pages = {889--920},
 title = {{The resolvent of an elliptic boundary problem}},
 url = {http://www.jstor.org/stable/10.2307/2373309},
 volume = {91},
 year = {1969}
 }
 @article{Hausenblas2003,
 author = {Hausenblas, Erika},
 file = {::},
 journal = {Potential Analysis},
 keywords = {numerical ap-,stochastic evolution equations,stochastic partial differential equations},
 number = {2},
 pages = {141--186},
 publisher = {Springer},
 title = {{Approximation for semilinear stochastic evolution equations}},
 url = {http://www.springerlink.com/index/U1242M1273831852.pdf},
 volume = {18},
 year = {2003}
 }
 @article{Bogachev2001,
 author = {Bogachev, Vladimir I. and Rockner, Michael and Wang, F.Y.},
 file = {::},
 journal = {Comptes Rendus de l'Academie des Sciences-Serie I-Mathematique},
 number = {4},
 pages = {333--338},
 publisher = {Paris: Gauthier-Villars, c1984-c2001.},
 title = {{Elliptic equations for invariant measures on Riemannian manifolds: existence and regularity of solutions}},
 url = {http://math.bnu.edu.cn/$\sim$wangfy/files/2001_02.pdf},
 volume = {332},
 year = {2001}
 }
 @article{Zhou2008,
 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.},
 author = {Zhou, Xiang and Ren, Weiqing and E, Weinan},
 doi = {10.1063/1.2830717},
 file = {::},
 issn = {0021-9606},
 journal = {The Journal of chemical physics},
 month = mar,
 number = {10},
 pages = {104111},
 pmid = {18345881},
 title = {{Adaptive minimum action method for the study of rare events.}},
 url = {http://www.ncbi.nlm.nih.gov/pubmed/18345881},
 volume = {128},
 year = {2008}
 }
 @article{Nualart2009,
 author = {Nualart, Eulalia and Viens, Frederi},
 doi = {10.1016/j.spa.2008.07.009},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 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},
 month = may,
 number = {5},
 pages = {1505--1540},
 publisher = {Elsevier B.V.},
 title = {{The fractional stochastic heat equation on the circle: Time regularity and potential theory}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908001233},
 volume = {119},
 year = {2009}
 }
 @article{Vasilach1973,
 author = {Vasilach, S.},
 file = {::},
 journal = {Publications de l'institut math\'{e}matique},
 number = {29},
 pages = {153--169},
 title = {{Solutions of some Parabolic Integro-differential Equations by means of the algebraic operational calculus of distributions}},
 volume = {15},
 year = {1973}
 }
 @article{Laetsch1975,
 author = {Laetsch, T},
 file = {::},
 journal = {Indiana University. Math. Journal},
 number = {7},
 pages = {651--658},
 title = {{Critical solutions of autonomous non linear boundary value problems}},
 url = {http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:critical+solutions+of+autonomous+nonlinear+boundary+value+problems#8},
 volume = {24},
 year = {1975}
 }
 @article{Rinaldi2000,
 author = {Rinaldi, Sergio and Scheffer, Marten},
 doi = {10.1007/s100210000045},
 file = {::},
 issn = {1432-9840},
 journal = {Ecosystems},
 keywords = {bation,bifurcation analysis,catastrophes,fast cycles,fast dynamics,quasi,singular pertur-,slow,steady state},
 month = nov,
 number = {6},
 pages = {507--521},
 title = {{Geometric Analysis of Ecological Models with Slow and Fast Processes}},
 url = {http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s100210000045},
 volume = {3},
 year = {2000}
 }
 @article{Carr1989,
 author = {Carr, J. and Pego, R. L.},
 file = {::},
 journal = {Communications on Pure and Applied Mathematics},
 number = {5},
 pages = {523--576},
 title = {{Metastable patterns in solutions of {$u_t=\epsilon^2u_{xx}-f(u)$}}},
 volume = {42},
 year = {1989}
 }
 @article{Angenent1988a,
 author = {Angenent, Sigurd B. and Fiedler, Bernold},
 doi = {10.1090/S0002-9947-1988-0940217-X},
 file = {::},
 issn = {0002-9947},
 journal = {Transactions of the American Mathematical Society},
 month = feb,
 number = {2},
 pages = {545--545},
 title = {{The dynamics of rotating waves in scalar reaction diffusion equations}},
 url = {http://www.ams.org/jourcgi/jour-getitem?pii=S0002-9947-1988-0940217-X},
 volume = {307},
 year = {1988}
 }
 @article{Joly2010,
 author = {Joly, Romain and Raugel, Genevi\`{e}ve},
 doi = {10.1016/j.anihpc.2010.09.001},
 file = {::},
 issn = {02941449},
 journal = {Annales de l'Institut Henri Poincare (C) Non Linear Analysis},
 month = nov,
 number = {6},
 pages = {1397--1440},
 publisher = {Elsevier Masson SAS},
 title = {{Generic Morse–Smale property for the parabolic equation on the circle}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0294144910000624},
 volume = {27},
 year = {2010}
 }
 @article{Lorenz1963,
 author = {Lorenz, Edward N.},
 file = {::},
 journal = {Journal of Atmospheric Science},
 pages = {130--141},
 title = {{Deterministic non-periodic flow}},
 url = {http://en.scientificcommons.org/19848251},
 volume = {20},
 year = {1963}
 }
 @article{Marcus1978,
 author = {Marcus, R.},
 file = {::},
 journal = {Journal of Functional Analysis},
 number = {3},
 pages = {275--286},
 publisher = {Elsevier},
 title = {{Parabolic It\^{o} equations with monotone nonlinearities}},
 url = {http://www.sciencedirect.com/science/article/pii/0022123678900319},
 volume = {29},
 year = {1978}
 }
 @article{Hairer2005,
 author = {Hairer, Martin and Stuart, Andrew M. and Voss, Jochen and Wiberg, P},
 file = {::},
 journal = {Communications in Mathematical Sciences},
 number = {4},
 pages = {587--603},
 publisher = {International Press of Boston},
 title = {{Analysis of SPDEs arising in path sampling. Part I: The Gaussian case}},
 url = {http://projecteuclid.org/euclid.cms/1144429334},
 volume = {3},
 year = {2005}
 }
 @article{gyongy99,
 author = {Gy{\"o}ngy, Istv{\'a}n},
 journal = {Potential Analysis},
 title = {{Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise II}},
 url = {http://www.springerlink.com/index/X644L10403753878.pdf},
 year = {1999}
 }
 @article{Danchin2011,
 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.},
 author = {Danchin, Etienne and Charmantier, Anne and Champagne, Frances A. and Mesoudi, Alex and Pujol, Benoit and Blanchet, Simon},
 doi = {10.1038/nrg3028},
 file = {::},
 issn = {1471-0064},
 journal = {Nature reviews. Genetics},
 month = jan,
 number = {7},
 pages = {475--86},
 pmid = {21681209},
 publisher = {Nature Publishing Group},
 title = {{Beyond DNA: integrating inclusive inheritance into an extended theory of evolution.}},
 url = {http://www.ncbi.nlm.nih.gov/pubmed/21681209},
 volume = {12},
 year = {2011}
 }
 @techreport{Blomker2010,
 author = {Bl\"{o}mker, D. and Jentzen, Arnulf},
 file = {::},
 institution = {Working paper},
 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},
 pages = {1--46},
 title = {{Galerkin approximations for the stochastic Burgers equation}},
 url = {http://opus.bibliothek.uni-augsburg.de/volltexte/2009/1444/},
 year = {2010}
 }
 @article{Chung1959,
 author = {Chung, K.L.},
 file = {::},
 pages = {629--639},
 title = {{On last exit times}},
 year = {1959}
 }
 @article{Schmeiser2001,
 author = {Schmeiser, C},
 file = {::},
 journal = {Mathematical Models and Methods in Applied Sciences},
 number = {1},
 pages = {43--56},
 title = {{ASYMPTOTIC FORMULAS FOR DISCRETE EIGENVALUE}},
 volume = {11},
 year = {2001}
 }
 @article{Jona-Lasinio1985,
 author = {Jona-Lasinio, G. and Mitter, PK},
 file = {::},
 journal = {Communications in Mathematical Physics},
 number = {3},
 pages = {409--436},
 publisher = {Springer},
 title = {{On the stochastic quantization of field theory}},
 url = {http://www.springerlink.com/index/L1G0588734G0R075.pdf},
 volume = {101},
 year = {1985}
 }
 @article{Eckmann2001c,
 author = {Eckmann, J.-P. and Hairer, Martin},
 file = {::;::;::},
 journal = {Nonlinearity},
 pages = {133},
 publisher = {IOP Publishing},
 title = {{Invariant measures for stochastic partial differential equations in unbounded domains}},
 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},
 volume = {14},
 year = {2001}
 }
 @article{Burghelea1992a,
 author = {Burghelea, D. and Friedlander, L. and Kappeler, T.},
 file = {::},
 journal = {Communications in Mathematical Physics},
 number = {2},
 pages = {431},
 publisher = {Springer},
 title = {{Erratum: On the determination of elliptic differential and finite difference operators in vector bundles over $S^1$}},
 url = {http://www.springerlink.com/index/k46538n72j561608.pdf},
 volume = {150},
 year = {1992}
 }
 @incollection{Grosche1993,
 archivePrefix = {arXiv},
 arxivId = {arXiv:hep-th/9302097v1},
 author = {Grosche, Christian},
 booktitle = {Arxiv preprint hep-th/9302097},
 eprint = {9302097v1},
 file = {::},
 number = {November},
 primaryClass = {arXiv:hep-th},
 title = {{An introduction into the Feynman path integral}},
 url = {http://arxiv.org/abs/hep-th/9302097},
 year = {1993}
 }
 @inproceedings{Albeverio2011,
 author = {Albeverio, Sergio and Mazzucchi, S.},
 booktitle = {Seminar on Stochastic Analysis, Random Fields and Applications VI},
 file = {::},
 number = {332},
 pages = {3--21},
 publisher = {Springer},
 title = {{The trace formula for the heat semigroup with polynomial potential}},
 url = {http://www.springerlink.com/index/X6654U4VL3G450K9.pdf},
 year = {2011}
 }
 @article{Fitzsimmons1988,
 author = {Fitzsimmons, P. J. and Getoor, R. K.},
 file = {::},
 journal = {Mathematische Annalen},
 number = {3},
 pages = {495--512},
 publisher = {Springer},
 title = {{On the potential theory of symmetric Markov processes}},
 url = {http://www.springerlink.com/index/V5836436X0352T13.pdf},
 volume = {281},
 year = {1988}
 }
 @article{millet.morien05,
 author = {Millet, Annie and Morien, Pierre-Luc},
 doi = {10.1016/j.spa.2005.02.004},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 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},
 month = jul,
 number = {7},
 pages = {1073--1106},
 title = {{On implicit and explicit discretization schemes for parabolic SPDEs in any dimension}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414905000189},
 volume = {115},
 year = {2005}
 }
 @article{Sturm2003,
 author = {Sturm, A},
 file = {::},
 journal = {Electronic Journal of Probability},
 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},
 number = {2000},
 pages = {1--39},
 title = {{On convergence of population processes in random environments to the stochastic heat equation with colored noise}},
 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/include/getdoc9eac.pdf?id=2912&article=1347&mode=pdf},
 year = {2003}
 }
 @article{Cox2011,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1103.1676v1},
 author = {Cox, J.T. and Durrett, Richard and Perkins, E.},
 eprint = {arXiv:1103.1676v1},
 file = {::},
 journal = {Arxiv preprint arXiv:1103.1676},
 keywords = {and phrases,evo-,interacting particle systems,lotka-volterra model,lutionary game theory,reaction diffusion equation,voter model},
 pages = {1--106},
 title = {{Voter model perturbations and reaction diffusion equations}},
 url = {http://arxiv.org/abs/1103.1676},
 year = {2011}
 }
 @article{chenal.millet97,
 author = {Chenal, F. and Millet, A.},
 journal = {Stochastic Process. Appl.},
 number = {2},
 pages = {161----186},
 title = {{Uniform large deviations for parabolic {SPDE}s and applications}},
 volume = {72},
 year = {1997}
 }
 @article{holling73,
 author = {Holling, C.S.},
 file = {::},
 journal = {Annual review of ecology and systematics},
 pages = {1--23},
 publisher = {JSTOR},
 title = {{Resilience and stability of ecological systems}},
 url = {http://www.jstor.org/stable/10.2307/2096802},
 volume = {4},
 year = {1973}
 }
 @article{Chung1973,
 author = {Chung, K.L.},
 file = {::},
 journal = {Ann. Inst. Fourier (Grenoble)},
 pages = {313--322},
 title = {{Probabilistic approach in potential theory to the equilibrium problem}},
 url = {http://archive.numdam.org/article/AIF_1973__23_3_313_0.pdf},
 volume = {23},
 year = {1973}
 }
 @article{Funaki2004d,
 author = {Funaki, Tadahisa},
 doi = {10.1214/009117904000000199},
 file = {::;::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 month = apr,
 number = {2},
 pages = {1228--1246},
 title = {{Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension}},
 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884850/ http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884849/},
 volume = {32},
 year = {2004}
 }
 @article{Garcia-Pelayo1997,
 author = {Garc\'{\i}a-Pelayo, Ricardo and Stadler, Peter F.},
 doi = {10.1016/S0167-2789(97)00091-2},
 file = {::},
 issn = {01672789},
 journal = {Physica D: Nonlinear Phenomena},
 keywords = {graph laplacian,isotropy,meta-stable states,rugged landscapes,xy-hamiltonian},
 month = sep,
 number = {2-4},
 pages = {240--254},
 title = {{Correlation length, isotropy and meta-stable states}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278997000912},
 volume = {107},
 year = {1997}
 }
 @article{Dimock1974,
 author = {Dimock, Jonathan and Glimm, James},
 file = {::},
 journal = {Advances in Mathematics},
 pages = {58--83},
 title = {{Mesures on schwartz distribution space and applications to $P(\phi)_2$ field theories}},
 volume = {12},
 year = {1974}
 }
 @article{Bellettini2005,
 author = {Bellettini, G. and {De Masi}, a. and Presutti, E.},
 doi = {10.1063/1.1990107},
 file = {::},
 issn = {00222488},
 journal = {Journal of Mathematical Physics},
 number = {8},
 pages = {083302},
 title = {{Energy levels of a nonlocal functional}},
 url = {http://link.aip.org/link/JMAPAQ/v46/i8/p083302/s1&Agg=doi},
 volume = {46},
 year = {2005}
 }
 @article{Billingsley1974,
 author = {Billingsley, P.},
 file = {::},
 journal = {The Annals of Probability},
 number = {5},
 pages = {749--791},
 publisher = {JSTOR},
 title = {{The probability theory of additive arithmetic functions}},
 url = {http://www.jstor.org/stable/10.2307/2959305},
 volume = {2},
 year = {1974}
 }
 @misc{Mattingly2007,
 author = {Mattingly, Jonathan C.},
 booktitle = {Saint-Flour lecture notes},
 file = {::},
 title = {{Ergodicity of dissipative spdes}},
 url = {http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:Ergodicity+of+Dissipative+SPDEs#0},
 year = {2007}
 }
 @article{Hairer2009c,
 author = {Hairer, Martin},
 file = {::},
 journal = {Arxiv preprint arXiv:0910.0315},
 number = {1},
 pages = {1--6},
 title = {{Hypoellipticity in infinite dimensions}},
 url = {http://arxiv.org/abs/0910.0315},
 year = {2009}
 }
 @article{Simon1977,
 author = {Simon, Barry},
 file = {::},
 journal = {Advances in Mathematics},
 number = {3},
 pages = {244--273},
 publisher = {Elsevier},
 title = {{Notes on infinite determinants of Hilbert space operators}},
 url = {http://www.sciencedirect.com/science/article/pii/0001870877900573},
 volume = {24},
 year = {1977}
 }
 @misc{Hur2008,
 archivePrefix = {arXiv},
 arxivId = {arXiv:0805.0079v1},
 author = {Hur, Jin and Min, Hyunsoo},
 eprint = {arXiv:0805.0079v1},
 file = {::},
 pages = {1--28},
 title = {{A Fast Way to Compute Functional Determinants of Radially Symmetric Partial Differential Operators in General Dimensions}},
 year = {2008}
 }
 @article{Getoor1973a,
 author = {Getoor, RK and Sharpe, MJ},
 file = {::},
 journal = {The Annals of Probability},
 number = {4},
 pages = {550--569},
 publisher = {Institute of Mathematical Statistics},
 title = {{Last exit times and additive functionals}},
 url = {http://projecteuclid.org/euclid.aop/1176996885},
 volume = {1},
 year = {1973}
 }
 @article{Cassandro1995,
 author = {Cassandro, Marzio and Marra, R. and Presutti, E.},
 file = {::},
 journal = {Journal of statistical physics},
 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},
 number = {3},
 pages = {1131--1138},
 publisher = {Springer},
 title = {{Corrections to the critical temperature in 2d Ising systems with Kac potentials}},
 url = {http://www.springerlink.com/index/7084R2NH31076G94.pdf},
 volume = {78},
 year = {1995}
 }
 @article{Scheffer2003,
 author = {Scheffer, Marten and Carpenter, Stephen R.},
 doi = {10.1016/j.tree.2003.09.002},
 file = {::},
 issn = {01695347},
 journal = {Trends in Ecology \& Evolution},
 month = dec,
 number = {12},
 pages = {648--656},
 title = {{Catastrophic regime shifts in ecosystems: linking theory to observation}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0169534703002787},
 volume = {18},
 year = {2003}
 }
 @article{Mehlig1992,
 author = {Mehlig, Bernhard and Forrest, Bruce M.},
 file = {::},
 journal = {Zeitschrift f\"{u}r Physik B},
 pages = {89--96},
 title = {{Universality in the critical two-dimensional $\phi^4$ model}},
 volume = {89},
 year = {1992}
 }
 @article{Duan2009,
 author = {Duan, Jinqiao and Millet, Annie},
 doi = {10.1016/j.spa.2008.10.004},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 keywords = {b,boussinesq equations,enard convection,equations,impact of noise on,large deviations,multiplicative noise,stochastic navier,stochastic pdes,stokes,system evolution},
 month = jun,
 number = {6},
 pages = {2052--2081},
 publisher = {Elsevier},
 title = {{Large deviations for the Boussinesq equations under random influences}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908001579},
 volume = {119},
 year = {2009}
 }
 @article{kirsten.mckane04,
 author = {Kirsten, Klaus and McKane, Alan J.},
 doi = {10.1088/0305-4470/37/16/014},
 file = {::},
 issn = {0305-4470},
 journal = {Journal of Physics A: Mathematical and General},
 month = apr,
 pages = {4649--4670},
 title = {{Functional determinants for general Sturm–Liouville problems}},
 url = {http://stacks.iop.org/0305-4470/37/i=16/a=014?key=crossref.7848aae42b4fc923ee79d511cf1cab33},
 volume = {37},
 year = {2004}
 }
 @article{brunovsky.chow84,
 author = {Brunovsky, P. and Chow, S.N.},
 file = {::},
 journal = {Journal of differential equations},
 number = {1},
 pages = {1--23},
 publisher = {Academic Press},
 title = {{Generic properties of stationary state solutions of reaction-diffusion equations}},
 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=9669009},
 volume = {53},
 year = {1984}
 }
 @phdthesis{Gentil2001,
 author = {Gentil, Ivan},
 file = {::},
 pages = {147},
 title = {{In\'{e}galit\'{e}s de Sobolev logarithmiques et hypercontractivit\'{e} en m\'{e}canique statistique et en EDP}},
 year = {2001}
 }
 @article{Bansaye2011,
 author = {Bansaye, Vincent and Lambert, Amaury},
 file = {::},
 number = {December},
 title = {{Past, growth and persistence of source-sink metapopulations}},
 url = {http://hal.archives-ouvertes.fr/hal-00639011/},
 year = {2011}
 }
 @article{Andrew2003,
 author = {Andrew, A.L.},
 file = {::},
 journal = {BIT Numerical Mathematics},
 keywords = {asymptotic correction,computation of higher eigenvalues,liouville problems,method,numerov,s,sturm},
 number = {3},
 pages = {485--503},
 publisher = {Springer},
 title = {{Asymptotic correction of more Sturm–Liouville eigenvalue estimates}},
 url = {http://www.springerlink.com/index/V68M787714507737.pdf},
 volume = {43},
 year = {2003}
 }
 @article{Blomker2004,
 author = {Bl\"{o}mker, D. and Hairer, Martin},
 file = {::},
 journal = {Communications in mathematical physics},
 number = {3},
 pages = {515--555},
 publisher = {Springer},
 title = {{Multiscale expansion of invariant measures for SPDEs}},
 url = {http://www.springerlink.com/index/HB88RP1WP5NNJTKP.pdf},
 volume = {251},
 year = {2004}
 }
 @article{faris.jonalasinio82,
 author = {Faris, William G. and Jona-Lasinio, G.},
 journal = {J. Phys. A},
 number = {10},
 pages = {3025----3055},
 title = {{Large fluctuations for a nonlinear heat equation with noise}},
 volume = {15},
 year = {1982}
 }
 @article{Cattiaux2010c,
 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.},
 author = {Cattiaux, Patrick and M\'{e}l\'{e}ard, Sylvie},
 doi = {10.1007/s00285-009-0285-4},
 file = {::},
 issn = {1432-1416},
 journal = {Journal of mathematical biology},
 keywords = {Animals,Behavior, Animal,Biostatistics,Computer Simulation,Computer Simulation: statistics & numerical data,Extinction, Biological,Models, Statistical,Population Dynamics,Stochastic Processes},
 month = jun,
 number = {6},
 pages = {797--829},
 pmid = {19649634},
 title = {{Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinction.}},
 url = {http://www.ncbi.nlm.nih.gov/pubmed/19649634},
 volume = {60},
 year = {2010}
 }
 @article{Berglund2001b,
 archivePrefix = {arXiv},
 arxivId = {arXiv:math/0111178v1},
 author = {Berglund, Nils},
 eprint = {0111178v1},
 file = {::},
 journal = {Arxiv preprint math/0111178},
 primaryClass = {arXiv:math},
 title = {{Perturbation theory of dynamical systems}},
 url = {http://arxiv.org/abs/math/0111178},
 year = {2001}
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 author = {Assaf, Michael and Mobilia, Mauro},
 eprint = {arXiv:1011.0322v1},
 file = {::},
 journal = {Journal of Theoretical Biology},
 number = {0},
 pages = {1--27},
 publisher = {Elsevier},
 title = {{Fixation of a deleterious allele under mutation pressure and finite selection intensity}},
 url = {http://www.sciencedirect.com/science/article/pii/S0022519311000373},
 year = {2011}
 }
 @article{Steiner2011,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1106.3573v1},
 author = {Steiner, J and Wieczoreck, H},
 eprint = {arXiv:1106.3573v1},
 file = {::},
 journal = {Arxiv preprint arXiv:},
 number = {1},
 pages = {1--26},
 title = {{The Formation and Coarsening of the Concertina Pattern}},
 url = {http://arxiv.org/abs/1106.3573},
 year = {2011}
 }
 @article{Meerson2011,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1008.4854v1},
 author = {Meerson, Baruch and Sasorov, P.V.},
 eprint = {arXiv:1008.4854v1},
 file = {::},
 journal = {Physical Review E},
 number = {1},
 pages = {011129},
 publisher = {APS},
 title = {{Extinction rates of established spatial populations}},
 url = {http://pre.aps.org/abstract/PRE/v83/i1/e011129},
 volume = {83},
 year = {2011}
 }
 @article{Fiedler2009,
 author = {Fiedler, Bernold and Rocha, Carlos},
 doi = {10.1515/CRELLE.2009.076},
 file = {::},
 issn = {0075-4102},
 journal = {Journal f\"{u}r die reine und angewandte Mathematik (Crelles Journal)},
 month = oct,
 number = {635},
 pages = {71--96},
 title = {{Connectivity and design of planar global attractors of Sturm type, I: Bipolar orientations and Hamiltonian paths}},
 url = {http://www.reference-global.com/doi/abs/10.1515/CRELLE.2009.076},
 volume = {2009},
 year = {2009}
 }
 @article{Gibbs2002,
 author = {Gibbs, A.L. and Su, F.E.},
 file = {::},
 journal = {International statistical review},
 number = {3},
 pages = {419--435},
 publisher = {Wiley Online Library},
 title = {{On choosing and bounding probability metrics}},
 url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1751-5823.2002.tb00178.x/abstract},
 volume = {70},
 year = {2002}
 }
 @article{Bertini2008,
 author = {Bertini, Lorenzo and Brassesco, Stella and Butt\`{a}, Paolo},
 file = {::},
 journal = {Archive for Rational Mechanics and Analysis},
 number = {3},
 pages = {477--516},
 publisher = {Springer},
 title = {{Dobrushin States in the $\phi_1^4$ Model}},
 url = {http://www.springerlink.com/index/7111352011336765.pdf},
 volume = {190},
 year = {2008}
 }
 @book{dellacherie.meyer87,
 address = {Paris},
 author = {Dellacherie, Claude and Meyer, Paul-Andr\'{e}},
 pages = {xii+378},
 publisher = {Hermann},
 title = {{Probabilit\'es et potentiel. {C}ha\-pitres {XII}--{XVI}.}},
 year = {1987}
 }
 @article{Voter1998,
 author = {Voter, Arthur},
 doi = {10.1103/PhysRevB.57.R13985},
 file = {::},
 issn = {0163-1829},
 journal = {Physical Review B},
 month = jun,
 number = {22},
 pages = {R13985--R13988},
 title = {{Parallel replica method for dynamics of infrequent events}},
 url = {http://link.aps.org/doi/10.1103/PhysRevB.57.R13985},
 volume = {57},
 year = {1998}
 }
 @article{Huillet2011,
 author = {Huillet, Thierry},
 doi = {10.1088/1742-5468/2011/02/P02016},
 file = {::},
 issn = {1742-5468},
 journal = {Journal of Statistical Mechanics: Theory and Experiment},
 month = feb,
 number = {02},
 pages = {P02016},
 title = {{On the Karlin–Kimura approaches to the Wright–Fisher diffusion with fluctuating selection}},
 url = {http://stacks.iop.org/1742-5468/2011/i=02/a=P02016?key=crossref.766bf36c47ddb77abbb765bb97545de0},
 volume = {2011},
 year = {2011}
 }
 @article{Rey-Bellet2002,
 author = {Rey-Bellet, Luc and Thomas, Lawrence E.},
 file = {::},
 journal = {Communications in mathematical physics},
 pages = {305--329},
 title = {{Exponential convergence to non-equilibrium stationary states in classical statistical mechanics}},
 url = {http://www.springerlink.com/index/qajgj1ejgp1j3ccr.pdf},
 volume = {225},
 year = {2002}
 }
 @article{Erbar2010,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1012.2718v1},
 author = {Erbar, Matthias},
 eprint = {arXiv:1012.2718v1},
 file = {::},
 journal = {Arxiv preprint arXiv:1012.2718},
 keywords = {invariant measure,large deviations,stochastic reaction-diffusion equation},
 number = {1},
 pages = {1--14},
 title = {{Low noise limit for the invariant measure of a multi-dimensional stochastic Allen-Cahn equation}},
 url = {http://arxiv.org/abs/1012.2718},
 year = {2010}
 }
 @article{Fix1967c,
 author = {Fix, George},
 file = {::;::},
 journal = {Journal of Mathematical Analysis and Applications},
 pages = {519--525},
 title = {{Asymptotic Eigenvalues of Sturm-Liouville Systems}},
 volume = {19},
 year = {1967}
 }
 @article{FRW04,
 author = {Fiedler, Bernold and Rocha, Carlos and Wolfrum, Matthias},
 doi = {10.1016/j.jde.2003.10.027},
 file = {::},
 issn = {00220396},
 journal = {Journal of Differential Equations},
 keywords = {global attractor,heteroclinic orbit,zero number},
 month = jun,
 number = {1},
 pages = {99--138},
 title = {{Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039604000683},
 volume = {201},
 year = {2004}
 }
 @article{Berglund2002,
 archivePrefix = {arXiv},
 arxivId = {arXiv:cond-mat/0110180v1},
 author = {Berglund, Nils and Gentz, Barbara},
 eprint = {0110180v1},
 file = {::},
 journal = {Journal of Physics A: Mathematical and General},
 keywords = {and phrases,bifurcation delay,double-well potential,dynamical hysteresis,exit time,first-,fokker,langevin equation,planck equation,scaling laws,stochastic resonance,white noise},
 pages = {2057},
 primaryClass = {arXiv:cond-mat},
 publisher = {IOP Publishing},
 title = {{Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems}},
 url = {http://iopscience.iop.org/0305-4470/35/9/301},
 volume = {35},
 year = {2002}
 }
 @inproceedings{levit.smilansky77,
 author = {Levit, S. and Smilansky, U.},
 booktitle = {Proc. Amer. Math. Soc},
 file = {::},
 number = {2},
 pages = {299--302},
 title = {{A theorem on infinite products of eigenvalues of Sturm–Liouville type operators}},
 url = {http://www.ams.org/journals/proc/1977-065-02/S0002-9939-1977-0457836-8/S0002-9939-1977-0457836-8.pdf},
 volume = {65},
 year = {1977}
 }
 @article{Majda1999,
 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.},
 author = {Majda, Andrew J. and Timofeyev, Ilya and Vanden-Eijnden, Eric},
 file = {::},
 issn = {0027-8424},
 journal = {Proceedings of the National Academy of Sciences of the United States of America},
 month = dec,
 number = {26},
 pages = {14687--91},
 pmid = {10611273},
 title = {{Models for stochastic climate prediction.}},
 url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=24708&tool=pmcentrez&rendertype=abstract},
 volume = {96},
 year = {1999}
 }
 @article{angenent86,
 author = {Angenent, Sigurd B.},
 file = {::},
 journal = {Journal of differential equations},
 pages = {427--442},
 title = {{The Morse-Smale property for a semi-linear parabolic equation}},
 url = {http://cat.inist.fr/?aModele=afficheN&cpsidt=8771440},
 volume = {62},
 year = {1986}
 }
 @article{Matkowsky1977,
 author = {Matkowsky, B.J. and Schuss, Z.},
 file = {::},
 journal = {SIAM Journal on Applied Mathematics},
 number = {2},
 pages = {365--382},
 publisher = {JSTOR},
 title = {{The exit problem for randomly perturbed dynamical systems}},
 url = {http://www.jstor.org/stable/10.2307/2100884},
 volume = {33},
 year = {1977}
 }
 @article{Albeverio2009,
 author = {Albeverio, Sergio and Mandrekar, V. and R\"{u}diger, B.},
 doi = {10.1016/j.spa.2008.03.006},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 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},
 month = mar,
 number = {3},
 pages = {835--863},
 title = {{Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian L\'{e}vy noise}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414908000604},
 volume = {119},
 year = {2009}
 }
 @article{\'Alvarez2000,
 archivePrefix = {arXiv},
 arxivId = {arXiv:cond-mat/9905034v1},
 author = {{\'A}lvarez, Luis Fern{\'a}ndez and Pla, Oscar and Chubykalo, Oskana},
 eprint = {9905034v1},
 file = {::},
 journal = {Physical Review B},
 pages = {1--4},
 primaryClass = {arXiv:cond-mat},
 title = {{Quasiperiodicity, bistability, and chaos in the Landau-Lifshitz equation}},
 url = {http://prb.aps.org/abstract/PRB/v61/i17/p11613_1},
 year = {2000}
 }
 @article{Berkov2005,
 author = {Berkov, D.V. and Gorn, N.L.},
 file = {::},
 journal = {Journal of magnetism and magnetic materials},
 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},
 number = {1},
 pages = {442--448},
 publisher = {Elsevier},
 title = {{Stochastic dynamic simulations of fast remagnetization processes: recent advances and applications}},
 url = {http://www.sciencedirect.com/science/article/pii/S0304885304018323},
 volume = {290},
 year = {2005}
 }
 @article{Bogachev2001a,
 author = {Bogachev, Vladimir I. and R\"{o}ckner, Michael and Wang, Feng-Yu},
 doi = {10.1016/S0021-7824(00)01187-9},
 file = {::},
 issn = {00217824},
 journal = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es},
 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},
 month = mar,
 number = {2},
 pages = {177--221},
 title = {{Elliptic equations for invariant measures on finite and infinite dimensional manifolds}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0021782400011879},
 volume = {80},
 year = {2001}
 }
 @article{gotts2007,
 author = {Gotts, N.M.},
 file = {::},
 journal = {Ecology and Society},
 keywords = {adaptive cycle,cross-scale interaction,panarchy,population,resilience,technology,world-},
 number = {1},
 pages = {24},
 title = {{Resilience, panarchy, and world-systems analysis}},
 url = {http://www.philadelphia.edu.jo/courses/SAD/ES-2007-2017.pdf},
 volume = {12},
 year = {2007}
 }
 @article{Korzec2007,
 author = {Korzec, M.D. and Evans, P.L. and M\"{u}nch, A. and Wagner, B},
 file = {::},
 journal = {Arxiv preprint arXiv:0712.2482},
 keywords = {convective cahn-hilliard,dynamical systems,exponential asymptotics,matching,quantum dots},
 pages = {1--32},
 title = {{Stationary solutions of driven fourth-and sixth-order Cahn-Hilliard type equations}},
 url = {http://arxiv.org/abs/0712.2482},
 year = {2007}
 }
 @article{Zitt2008,
 author = {Zitt, Pierre-Andr\'{e}},
 doi = {10.1016/j.spa.2007.04.002},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 keywords = {capacity criterion,e inequality,measure,simulated annealing,weak poincar},
 month = jan,
 number = {1},
 pages = {76--119},
 title = {{Annealing diffusions in a potential function with a slow growth}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0304414907000555},
 volume = {118},
 year = {2008}
 }
 @article{Hirsch1984,
 author = {Hirsch, M.W.},
 file = {::},
 journal = {Bull, American Mathematical Society},
 number = {1},
 pages = {1--64},
 title = {{The dynamical systems approach to differential equations}},
 url = {http://www.ams.org/journals/bull/1984-11-01/S0273-0979-1984-15236-4/S0273-0979-1984-15236-4.pdf},
 volume = {11},
 year = {1984}
 }
 @article{Kawabi2005,
 author = {Kawabi, Hiroshi},
 file = {::},
 journal = {Potential Analysis},
 keywords = {gradient estimate,parabolic harnack inequality,spde,varadhan type small time},
 number = {1},
 pages = {61--84},
 publisher = {Springer},
 title = {{The parabolic Harnack inequality for the time dependent Ginzburg–Landau type SPDE and its application}},
 url = {http://www.springerlink.com/index/R255173448J35035.pdf},
 volume = {22},
 year = {2005}
 }
 @article{Berglund2007c,
 archivePrefix = {arXiv},
 arxivId = {arXiv:math/0611648v2},
 author = {Berglund, Nils and Fernandez, Bastien and Gentz, Barbara},
 eprint = {0611648v2},
 file = {::;::},
 journal = {Nonlinearity},
 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},
 pages = {2583},
 primaryClass = {arXiv:math},
 publisher = {IOP Publishing},
 title = {{Metastability in interacting nonlinear stochastic differential equations: II. Large-N behaviour}},
 url = {http://iopscience.iop.org/0951-7715/20/11/006 http://iopscience.iop.org/0951-7715/20/11/007},
 volume = {20},
 year = {2007}
 }
 @article{Kolmogorov1983,
 author = {Kolmogorov, A},
 file = {::},
 journal = {Probability theory and mathematical statistics},
 title = {{On logical foundations of probability theory}},
 url = {http://www.springerlink.com/index/C280G6665G4MH441.pdf},
 year = {1983}
 }
 @book{VandenBerg2003,
 author = {van den Berg, J. B. and Vandervorst, R. C. and Ghrist, R. W.},
 booktitle = {Inventiones Mathematicae},
 doi = {10.1007/s00222-002-0277-0},
 file = {::},
 isbn = {0022200202770},
 issn = {0020-9910},
 month = may,
 number = {2},
 pages = {369--432},
 title = {{Morse theory on spaces of braids and Lagrangian dynamics}},
 url = {http://www.springerlink.com/Index/10.1007/s00222-002-0277-0},
 volume = {152},
 year = {2003}
 }
 @article{Liu2003,
 author = {Liu, D.},
 file = {::},
 journal = {Communications in Mathematical Sciences},
 keywords = {ginzburg-landau equation,rate of convergence,space-time white noise,spectral method,stochastic partial differential equa-,tions},
 number = {2},
 pages = {361--375},
 publisher = {International Press of Boston},
 title = {{Convergence of the spectral method for stochastic Ginzburg-Landau equation driven by space-time white noise}},
 url = {http://projecteuclid.org/euclid.cms/1118152076},
 volume = {1},
 year = {2003}
 }
 @article{assaf.meerson10,
 archivePrefix = {arXiv},
 arxivId = {arXiv:0907.0070v3},
 author = {Assaf, Michael and Meerson, Baruch},
 eprint = {arXiv:0907.0070v3},
 file = {::},
 journal = {Physical Review E},
 number = {2},
 pages = {021116},
 publisher = {APS},
 title = {{Extinction of metastable stochastic populations}},
 url = {http://pre.aps.org/abstract/PRE/v81/i2/e021116},
 volume = {81},
 year = {2010}
 }
 @article{Budhiraja2008,
 author = {Budhiraja, Amarjit and Dupuis, Paul and Maroulas, Vasileios},
 doi = {10.1214/07-AOP362},
 file = {::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 month = jul,
 number = {4},
 pages = {1390--1420},
 title = {{Large deviations for infinite dimensional stochastic dynamical systems}},
 url = {http://projecteuclid.org/euclid.aop/1217360973},
 volume = {36},
 year = {2008}
 }
 @article{lelievre12,
 author = {Leli\`{e}vre, Tony},
 file = {::},
 journal = {Arxiv preprint arXiv:1201.3775},
 pages = {1--19},
 title = {{Two mathematical tools to analyze metastable stochastic processes}},
 url = {http://arxiv.org/abs/1201.3775},
 year = {2012}
 }
 @article{Paine1981,
 author = {Paine, JW and Hoog, FR},
 file = {::},
 journal = {Computing},
 pages = {123--139},
 title = {{On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems}},
 url = {http://www.springerlink.com/index/Y63P073789N33840.pdf},
 volume = {139},
 year = {1981}
 }
 @misc{barret07,
 author = {Barret, Florent},
 title = {{Metastability: Application to a model of sharp asymptotics for capacities and exit/hitting times; Master thesis.}},
 year = {2007}
 }
 @article{Weissman1997,
 author = {Weissman, MB},
 file = {::},
 journal = {Physica D: Nonlinear Phenomena},
 keywords = {charge-density wave,f noise,hierarchy,l,spin-glass,vortex noise},
 number = {2-4},
 pages = {421--429},
 publisher = {Elsevier},
 title = {{Sorting out landscapes by mesoscopic noise}},
 url = {http://www.sciencedirect.com/science/article/pii/S0167278997001103},
 volume = {107},
 year = {1997}
 }
 @article{chafee.infante74,
 author = {Chafee, N. and Infante, EF},
 file = {::},
 journal = {AMERICAN MATHEMATICAL SOCIETY},
 number = {1},
 pages = {49--52},
 title = {{Bifurcation and stability for a nonlinear parabolic partial differential equation}},
 url = {http://www.ams.org/journals/bull/1974-80-01/S0002-9904-1974-13349-5/S0002-9904-1974-13349-5.pdf},
 volume = {80},
 year = {1974}
 }
 @article{Imkeller2006a,
 author = {Imkeller, Peter and Pavlyukevich, Ilya},
 doi = {10.1088/0305-4470/39/15/L01},
 file = {::},
 issn = {0305-4470},
 journal = {Journal of Physics A: Mathematical and General},
 month = apr,
 number = {15},
 pages = {L237--L246},
 title = {{L\'{e}vy flights: transitions and meta-stability}},
 url = {http://stacks.iop.org/0305-4470/39/i=15/a=L01?key=crossref.f804f9c4a34272b0d15b78e8a53997ea},
 volume = {39},
 year = {2006}
 }
 @article{Hairer2011a,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1008.1708v1},
 author = {Hairer, M.},
 doi = {10.1002/cpa.20383},
 eprint = {arXiv:1008.1708v1},
 file = {::;::},
 issn = {00103640},
 journal = {Communications on Pure and Applied Mathematics},
 month = jul,
 pages = {n/a--n/a},
 title = {{Rough stochastic PDEs}},
 url = {http://doi.wiley.com/10.1002/cpa.20383},
 year = {2011}
 }
 @article{JKO97,
 author = {Jordan, Richard and Kinderlehrer, David and Otto, Felix},
 file = {::},
 journal = {Physica D: Nonlinear Phenomena},
 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},
 pages = {265--271},
 title = {{Free energy and the Fokker-Planck equation}},
 url = {http://www.sciencedirect.com/science/article/pii/S0167278997000936},
 volume = {107},
 year = {1997}
 }
 @article{Neiman-Zade1999,
 author = {Neiman-Zade, MI and Shkalikov, A. A.},
 file = {::},
 journal = {Mathematical Notes},
 keywords = {distribution,generalized function,laplace operator,point interaction,polyharmonic operator,resolvent identities,schrhdinger operator,singular perturbation},
 number = {5},
 pages = {599--607},
 publisher = {Springer},
 title = {{Schr\"{o}dinger operators with singular potentials from the space of multiplicators}},
 url = {http://www.springerlink.com/index/96842604585N5M43.pdf},
 volume = {66},
 year = {1999}
 }
 @article{Day1990,
 author = {Day, Martin V.},
 doi = {10.1016/0022-247X(90)90389-W},
 file = {::},
 issn = {0022247X},
 journal = {Journal of Mathematical Analysis and Applications},
 month = mar,
 number = {1},
 pages = {134--153},
 title = {{Large deviations results for the exit problem with characteristic boundary}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/0022247X9090389W},
 volume = {147},
 year = {1990}
 }
 @article{Guerra1975,
 author = {Guerra, F. and Rosen, L and Simon, Barry},
 file = {::},
 journal = {The Annals of Mathematics},
 number = {1},
 pages = {111--189},
 publisher = {JSTOR},
 title = {{The $P (\varphi)_2$ Euclidean quantum field theory as classical statistical mechanics}},
 url = {http://www.jstor.org/stable/10.2307/1970988},
 volume = {101},
 year = {1975}
 }
 @misc{Kuksin2011,
 author = {Kuksin, Sergei},
 booktitle = {Quantum},
 file = {::},
 pages = {1--16},
 title = {{Quantum averaging , quantum KAM and quantum diffusion .}},
 year = {2011}
 }
 @article{Farmer1971,
 author = {Farmer, C},
 doi = {10.1016/0022-247X(71)90172-7},
 file = {::},
 issn = {0022247X},
 journal = {Journal of Mathematical Analysis and Applications},
 month = apr,
 number = {1},
 pages = {228--232},
 title = {{A certain sequence of infinite determinants}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/0022247X71901727},
 volume = {34},
 year = {1971}
 }
 @article{Freidlin2010,
 author = {Freidlin, Mark I. and Koralov, L.},
 doi = {10.1016/j.spa.2010.03.006},
 file = {::},
 issn = {03044149},
 journal = {Stochastic Processes and their Applications},
 keywords = {metastability,nonlinear perturbations},
 month = jul,
 number = {7},
 pages = {1194--1214},
 publisher = {Elsevier B.V.},
 title = {{Metastability for nonlinear random perturbations of dynamical systems}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S030441491000075X},
 volume = {120},
 year = {2010}
 }
 @article{Serfaty2009,
 author = {Serfaty, Sylvia},
 file = {::},
 journal = {Comm. Appl. Nonlinear Anal., to appear},
 pages = {1--30},
 title = {{Gamma-convergence of gradient flows on Hilbert and metric spaces and applications}},
 url = {http://www.ann.jussieu.fr/serfaty/gcv-erice2.pdf},
 year = {2009}
 }
 @article{brassesco91,
 author = {Brassesco, Stella},
 file = {::},
 journal = {Stochastic processes and their applications},
 pages = {33--53},
 title = {{Some results on small random perturbations of an infinite dimensional dynamical system}},
 url = {http://www.sciencedirect.com/science/article/pii/030441499190071J},
 volume = {38},
 year = {1991}
 }
 @book{davies89,
 author = {Davies, E. B.},
 pages = {x+197},
 publisher = {Cambridge University Press},
 title = {{Heat kernels and spectral theory}},
 year = {1989}
 }
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 author = {Otto, Felix and Reznikoff, Maria G.},
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 journal = {Journal of Differential Equations},
 keywords = {coarsening rates,dynamic metastability,energy methods,nonlinear partial differential equations},
 month = jun,
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 title = {{Slow motion of gradient flows}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039607000824},
 volume = {237},
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 }
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 author = {Voros, A.},
 file = {::},
 title = {{Spectre de l'equation de schrodinger et methode BKW}},
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 journal = {Journal of Functional Analysis},
 keywords = {eigenvalue asymptotics,liouville operators,singular potentials,sturm},
 month = sep,
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 pages = {27--57},
 title = {{Eigenvalue asymptotics for Sturm–Liouville operators with singular potentials}},
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 author = {Cattiaux, Patrick and Guillin, Arnaud},
 file = {::},
 keywords = {26d10,47d07,60g10,60j60,e inequality,logarithmic sobolev inequality,lyapunov condition,msc 2000,poincar,transportation information inequality},
 pages = {1--11},
 title = {{Functional Inequalities via Lyapunov conditions}},
 url = {http://hal.archives-ouvertes.fr/docs/00/44/61/04/PDF/cg-procgrenoble_2.pdf},
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 author = {Wolfrum, Matthias},
 file = {::},
 journal = {Journal of Dynamics and Differential Equations},
 keywords = {attractors,heteroclinic orbits,meandric permutations,morse-smale systems,nodal properties,scalar semilinear equations},
 number = {1},
 pages = {207--241},
 title = {{Geometry of heteroclinic cascades in scalar parabolic differential equations}},
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 journal = {Arxiv preprint math/0111178},
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 title = {{Perturbation theory of dynamical systems}},
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 year = {2001}
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 keywords = {brownian motor,circulation,detailed balance,entropy production,fluctuation theorem,periodical reversibility,time-periodic markov chain},
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 pages = {831--859},
 title = {{A Simple Discrete Model of Brownian Motors: Time-periodic Markov Chains}},
 url = {http://www.springerlink.com/index/10.1007/s10955-006-9099-6},
 volume = {123},
 year = {2006}
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 publisher = {Institute of Mathematical Statistics},
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 author = {Martinelli, Fabio and Olivieri, Enzo and Scoppola, Elisabetta},
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 journal = {Journal of Statistical Physics},
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 number = {3},
 pages = {477--504},
 publisher = {Springer},
 title = {{Small random perturbations of finite-and infinite-dimensional dynamical systems: unpredictability of exit times}},
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 author = {Hairer, Martin and Mattingly, Jonathan C.},
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 pages = {658--738},
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 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/include/getdoc4164.pdf?id=5978&article=2206&mode=pdf},
 volume = {16},
 year = {2008}
 }
 @article{brunovsky.polacik97,
 author = {Brunovsky, P. and Pol\'{a}cik, P.},
 file = {::},
 journal = {Journal of differential equations},
 number = {1},
 pages = {129--181},
 publisher = {Academic Press},
 title = {{The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension}},
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 year = {1997}
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 @misc{TheMendeleySupportTeam2011,
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 address = {London},
 author = {{The Mendeley Support Team}},
 booktitle = {Mendeley Desktop},
 file = {::},
 keywords = {Mendeley,how-to,user manual},
 pages = {1--16},
 publisher = {Mendeley Ltd.},
 title = {{Getting Started with Mendeley}},
 url = {http://www.mendeley.com},
 year = {2011}
 }
 @article{Pacard2011,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1102.3446v1},
 author = {Pacard, Frank and Wei, Juncheng},
 eprint = {arXiv:1102.3446v1},
 file = {::},
 journal = {Arxiv preprint arXiv:1102.3446},
 keywords = {allen-cahn equation,and phrases,infinite-,multiple-end solutions,toda system},
 pages = {1--30},
 title = {{Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones}},
 url = {http://arxiv.org/abs/1102.3446},
 year = {2011}
 }
 @article{VandenBerg2011,
 author = {van den Berg, J. B. and Kram\'{a}r, M. and Vandervorst, R. C.},
 file = {::},
 journal = {SIAM Journal on Applied Dynamical Systems},
 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},
 number = {2},
 pages = {510},
 title = {{The Order of Bifurcation Points in Fourth Order Conservative Systems via Braids}},
 url = {http://www.few.vu.nl/$\sim$RCAM.van.der.Vorst/PAPERS/BKV-2.pdf},
 volume = {10},
 year = {2011}
 }
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 author = {Eckmann, J.-P. and Hairer, Martin},
 file = {::},
 journal = {Nonlinearity},
 number = {133},
 title = {{Invariant measures for stochastic partial differential}},
 volume = {14},
 year = {2001}
 }
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 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},
 doi = {10.1214/09-AOP451},
 file = {::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 month = sep,
 number = {5},
 pages = {1926--1969},
 title = {{Quasi-stationary distributions and diffusion models in population dynamics}},
 url = {http://projecteuclid.org/euclid.aop/1253539860},
 volume = {37},
 year = {2009}
 }
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 author = {Kramers, HA},
 file = {::},
 journal = {Physica},
 title = {{Brownian motion in a field of force and the diffusion model of chemical reactions}},
 url = {http://www.sciencedirect.com/science/article/pii/S0031891440900982},
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 @article{Bakhtin2007,
 author = {Bakhtin, Yuri and Mattingly, Jonathan C.},
 doi = {10.1016/j.jfa.2007.02.011},
 file = {::},
 issn = {00221236},
 journal = {Journal of Functional Analysis},
 keywords = {degenerate stochastic partial differential,equations,malliavin calculus,smooth densities,spdes,stochastic},
 month = aug,
 number = {2},
 pages = {307--353},
 title = {{Malliavin calculus for infinite-dimensional systems with additive noise}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123607000559},
 volume = {249},
 year = {2007}
 }
 @article{Hairer2008b,
 author = {Hairer, Martin and Pardoux, Etienne},
 doi = {10.1016/j.jfa.2008.04.014},
 file = {::},
 issn = {00221236},
 journal = {Journal of Functional Analysis},
 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},
 month = nov,
 number = {9},
 pages = {2462--2487},
 publisher = {Elsevier Inc.},
 title = {{Homogenization of periodic linear degenerate PDEs}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123608001699},
 volume = {255},
 year = {2008}
 }
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 author = {Albeverio, Sergio and Mazzucchi, S.},
 file = {::},
 journal = {Journal of statistical physics},
 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},
 number = {1},
 pages = {191--215},
 publisher = {Springer},
 title = {{Some new developments in the theory of path integrals, with applications to quantum theory}},
 url = {http://www.springerlink.com/index/N85781GRQ00507H3.pdf},
 volume = {115},
 year = {2004}
 }
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 author = {Morato, L.M. and Ugolini, Stefania},
 file = {::},
 pages = {1--14},
 publisher = {Taylor & Francis},
 title = {{Stochastic quantization of finite dimensional systems with electromagnetic interactions}},
 url = {http://www.tandfonline.com/doi/abs/10.1080/17442508.2010.512975},
 year = {2011}
 }
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 author = {Pakin, Scott},
 booktitle = {Network},
 file = {::},
 number = {November},
 title = {{The comprehensive LATEX symbol list}},
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 archivePrefix = {arXiv},
 arxivId = {arXiv:1104.2129v1},
 author = {Ferrari, Patrik L. and Frings, Ren\'{e}},
 eprint = {arXiv:1104.2129v1},
 file = {::},
 journal = {Journal of Statistical Physics},
 pages = {1--28},
 publisher = {Springer},
 title = {{Finite time corrections in KPZ growth models}},
 url = {http://www.springerlink.com/index/N435757L2278270K.pdf},
 year = {2011}
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 author = {E, Weinan and Vanden-Eijnden, Eric},
 doi = {10.1007/s10955-005-9003-9},
 file = {::},
 issn = {0022-4715},
 journal = {Journal of Statistical Physics},
 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},
 month = may,
 number = {3},
 pages = {503--523},
 title = {{Towards a Theory of Transition Paths}},
 url = {http://www.springerlink.com/index/10.1007/s10955-005-9003-9},
 volume = {123},
 year = {2006}
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 author = {Doss, H and Royer, G},
 file = {::},
 journal = {Probability Theory and Related Fields},
 number = {1},
 pages = {107--124},
 publisher = {Springer},
 title = {{Processus de diffusion associe aux mesures de Gibbs sur $R^{Z^d}$}},
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 @article{Maragliano2006,
 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.},
 author = {Maragliano, Luca and Fischer, Alexander and Vanden-Eijnden, Eric and Ciccotti, Giovanni},
 doi = {10.1063/1.2212942},
 file = {::},
 issn = {0021-9606},
 journal = {The Journal of chemical physics},
 month = jul,
 number = {2},
 pages = {24106},
 pmid = {16848576},
 title = {{String method in collective variables: minimum free energy paths and isocommittor surfaces.}},
 url = {http://www.ncbi.nlm.nih.gov/pubmed/16848576},
 volume = {125},
 year = {2006}
 }
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 author = {Quer-Sardanyons, Llu\'{\i}s and Sanz-Sol\'{e}, Marta},
 doi = {10.1007/s11118-005-9002-0},
 file = {::},
 issn = {0926-2601},
 journal = {Potential Analysis},
 keywords = {discretisation schemes,stochastic partial differential equations,wave equation},
 month = may,
 number = {4},
 pages = {303--332},
 title = {{Space Semi-Discretisations for a Stochastic Wave Equation}},
 url = {http://www.springerlink.com/index/10.1007/s11118-005-9002-0},
 volume = {24},
 year = {2006}
 }
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 author = {Valent, V.},
 file = {::},
 journal = {Rend. Sem. Mat. Univ. Padova},
 pages = {63--73},
 title = {{A property of multiplication in Sobolev spaces. Some applications}},
 url = {http://archive.numdam.org/article/RSMUP_1985__74__63_0.pdf},
 volume = {74},
 year = {1985}
 }
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 archivePrefix = {arXiv},
 arxivId = {arXiv:1104.0720v2},
 author = {Ryser, Marc D. and Nigam, Nilima and Tupper, Paul F.},
 eprint = {arXiv:1104.0720v2},
 file = {::;::},
 keywords = {allen-cahn equation,numerical,stochastic pdes,well-posedness,white noise},
 pages = {1--20},
 title = {{On the well-posedness of the stochastic Allen-Cahn equation in two dimensions}},
 year = {2011}
 }
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 author = {Funaki, Tadahisa},
 doi = {10.1214/009117904000000180},
 file = {::},
 issn = {0091-1798},
 journal = {The Annals of Probability},
 month = apr,
 number = {2},
 pages = {1201--1227},
 title = {{Zero temperature limit for interacting Brownian particles. I. Motion of a single body}},
 url = {http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1084884849/},
 volume = {32},
 year = {2004}
 }
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 issn = {01672789},
 journal = {Physica D: Nonlinear Phenomena},
 keywords = {gibbs-boltzmann partition function,hierarchical landscapes,hypersurface,multiscale analysis,replica formalism,rugged energy,tap solutions},
 month = sep,
 number = {2-4},
 pages = {151--155},
 title = {{Multiscale analysis of hierarchical landscapes}},
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 year = {1997}
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 author = {Sugiura, Makoto},
 file = {::},
 journal = {Nagoya Mathematical Journal},
 pages = {137--154},
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 archivePrefix = {arXiv},
 arxivId = {arXiv:1011.1523v1},
 author = {Bianconi, Ginestra and Rahmede, Christoph},
 eprint = {arXiv:1011.1523v1},
 file = {::},
 journal = {Arxiv preprint arXiv:1011.1523},
 number = {1},
 pages = {1--8},
 title = {{Quantum mechanical formalism for biological evolution}},
 url = {http://arxiv.org/abs/1011.1523},
 year = {2010}
 }
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 archivePrefix = {arXiv},
 arxivId = {arXiv:1009.6077v1},
 author = {Smirnov, Stanislav},
 eprint = {arXiv:1009.6077v1},
 file = {::},
 journal = {Arxiv preprint arXiv:1009.6077},
 keywords = {avoiding walk,conformal invariance,discrete analytic function,discrete complex analysis,ising model,self-},
 title = {{Discrete complex analysis and probability}},
 url = {http://arxiv.org/abs/1009.6077},
 year = {2010}
 }
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 author = {Port, Sidney C. and Stone, Charles J.},
 pages = {xii+236},
 publisher = {Academic Press},
 title = {{Brownian motion and classical potential theory}},
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 @article{Ren2005,
 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.},
 author = {Ren, Weiqing and Vanden-Eijnden, Eric and Maragakis, Paul and E, Weinan},
 doi = {10.1063/1.2013256},
 file = {::},
 issn = {0021-9606},
 journal = {The Journal of chemical physics},
 keywords = {Alanine,Alanine: chemistry,Algorithms,Computer Simulation,Dipeptides,Dipeptides: chemistry,Isomerism,Models, Chemical,Models, Molecular,Molecular Conformation,Temperature,Thermodynamics},
 month = oct,
 number = {13},
 pages = {134109},
 pmid = {16223277},
 title = {{Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide.}},
 url = {http://www.ncbi.nlm.nih.gov/pubmed/16223277},
 volume = {123},
 year = {2005}
 }
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 author = {Martinelli, F. and Sbano, L. and Scoppola, E.},
 journal = {Stochastics Stochastics Rep.},
 number = {3-4},
 pages = {253----272},
 title = {{Small random perturbation of dynamical systems: recursive multiscale analysis}},
 volume = {49},
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 author = {Eckmann, J-p and Hairer, M},
 file = {::},
 journal = {Nonlinearity},
 pages = {133},
 publisher = {IOP Publishing},
 title = {{Invariant measures for stochastic partial differential equations in unbounded domains}},
 url = {http://iopscience.iop.org/0951-7715/14/1/308},
 volume = {14},
 year = {2001}
 }
 @article{Hinz2009a,
 author = {Hinz, Michael and Z\"{a}hle, Martina},
 doi = {10.1016/j.jfa.2009.02.006},
 file = {::},
 issn = {00221236},
 journal = {Journal of Functional Analysis},
 keywords = {fractional brownian sheet,fractional calculus,semigroups,stochastic partial differential equations},
 month = may,
 number = {10},
 pages = {3192--3235},
 publisher = {Elsevier Inc.},
 title = {{Gradient type noises II – Systems of stochastic partial differential equations}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S0022123609000706},
 volume = {256},
 year = {2009}
 }
 @article{Chekroun2011,
 author = {Chekroun, Micka\"{e}l D. and Simonnet, Eric and Ghil, Michael},
 doi = {10.1016/j.physd.2011.06.005},
 file = {::},
 issn = {01672789},
 journal = {Physica D: Nonlinear Phenomena},
 month = oct,
 number = {21},
 pages = {1685--1700},
 publisher = {Elsevier B.V.},
 title = {{Stochastic climate dynamics: Random attractors and time-dependent invariant measures}},
 url = {http://linkinghub.elsevier.com/retrieve/pii/S016727891100145X},
 volume = {240},
 year = {2011}
 }
 @article{Kleinhans2011,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1011.1109v1},
 author = {Kleinhans, David and Jonsson, P.R.},
 eprint = {arXiv:1011.1109v1},
 file = {::},
 journal = {Journal of Theoretical Biology},
 keywords = {connectivity matrix,dispersal network,metapopulation viability,symmetry},
 publisher = {Elsevier},
 title = {{On the impact of dispersal asymmetry on metapopulation persistence}},
 url = {http://www.sciencedirect.com/science/article/pii/S0022519311004589},
 year = {2011}
 }
 @article{Getoor1973,
 author = {Getoor, R. K. and Sharpe, M. J.},
 file = {::},
 journal = {The Annals of Probability},
 number = {4},
 pages = {1973},
 title = {{Last exit times and additive functionals}},
 url = {http://projecteuclid.org/euclid.aop/1176996885},
 volume = {1},
 year = {1973}
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 @article{Hairer2012,
 archivePrefix = {arXiv},
 arxivId = {arXiv:1202.3094v1},
 author = {Hairer, Martin and Maas, Jan and Weber, Hendrik},
 eprint = {arXiv:1202.3094v1},
 file = {::},
 journal = {Society},
 pages = {1--75},
 title = {{Approximating rough stochastic pdes}},
 year = {2012}
 }
 @misc{Hairer,
 author = {Hairer, Martin},
 file = {::},
 number = {x},
 pages = {1--3},
 title = {{Ergodic theory for infinite dimensional stochastic processes}}
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 @article{Gilbert2004,
 author = {Gilbert, TL},
 file = {::},
 journal = {Magnetics, IEEE Transactions on},
 number = {6},
 pages = {3443--3449},
 title = {{A phenomenological theory of damping in ferromagnetic materials}},
 url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1353448},
 volume = {40},
 year = {2004}
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 @article{Dalang2007,
 author = {Dalang, Robert C. and Khoshnevisan, Davar and Nualart, Eulalia},
 file = {::},
 journal = {ALEA. Latin American Journal of Probability and Mathematical Statistics},
 pages = {231--271},
 title = {{Hitting probabilities for systems of non-linear stochastic heat equations with additive noise}},
 url = {http://arxiv.org/abs/math/0702710},
 volume = {3},
 year = {2007}
 }
 @article{Cattiaux2010d,
 author = {Cattiaux, Patrick and Guillin, Arnaud and Roberto, Cyril},
 file = {::},
 journal = {Electronic},
 keywords = {1,26d10,39b62,47d07,60g10,60j60,e inequality,introduction and main results,msc 2010,poincar,rate of convergence},
 pages = {1--13},
 title = {{Poincar\'{e} inequality and the Lp convergence of semi-groups}},
 url = {http://www.emis.ams.org/journals/EJP-ECP/_ejpecp/ECP/include/getdocc479.pdf?id=5390&article=2212&mode=pdf},
 volume = {2},
 year = {2010}
 }
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 author = {Carron, G},
 file = {::},
 journal = {American journal of mathematics},
 number = {2},
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