F. Barret, Sharp asymptotics of metastable transition times for one dimensional SPDEs, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.51, issue.1, 2012.
DOI : 10.1214/13-AIHP575
URL : https://hal.archives-ouvertes.fr/hal-00661733

F. Barret, A. Bovier, and S. Méléard, Uniform estimates for metastable transition times in a coupled bistable system, Electron, J. Probab, vol.15, pp.323-345, 2010.

A. Bovier, M. Eckhoff, V. Gayrard, and M. Klein, Metastability in Reversible Diffusion Processes I: Sharp Asymptotics for Capacities and Exit Times, Journal of the European Mathematical Society, vol.6, issue.4, pp.399-424, 2004.
DOI : 10.4171/JEMS/14
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.3744

[. Berglund, Kramers' law: Validity, derivations and generalisations, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00604399

[. Berglund, B. Fernandez, and B. Gentz, Metastability in interacting nonlinear stochastic differential equations: I. From weak coupling to synchronization, Nonlinearity, vol.20, issue.11, pp.2551-2581, 2007.
DOI : 10.1088/0951-7715/20/11/006
URL : https://hal.archives-ouvertes.fr/hal-00115416

N. Berglund and B. Gentz, Anomalous behavior of the Kramers rate at bifurcations in classical field theories, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.5, p.52001, 2009.
DOI : 10.1088/1751-8113/42/5/052001
URL : https://hal.archives-ouvertes.fr/hal-00321846

A. Bovier, V. Gayrard, and M. Klein, Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues, Journal of the European Mathematical Society, vol.7, issue.1, pp.69-99, 2005.
DOI : 10.4171/JEMS/22

D. Blömker and A. Jentzen, Galerkin approximations for the stochastic Burgers equation, to appear in SIAM, J. Numer. Anal, 2013.

Y. Colin-deverdì-ere, D. Et-intégrales-de-fresnel, and A. , D??terminants et int??grales de Fresnel, Annales de l???institut Fourier, vol.49, issue.3, pp.861-881, 1998.
DOI : 10.5802/aif.1696

S. Cerrai, Elliptic and parabolic equations in with coefficients having polynomial growth, Communications in Partial Differential Equations, vol.45, issue.1-2, pp.281-317, 1996.
DOI : 10.1007/BF02573496

E. [. Chafee and . Infante, A bifurcation problem for a nonlinear partial differential equation of parabolic type, Applicable Anal, pp.17-37, 1974.

[. Chenal and A. Millet, Uniform large deviations for parabolic SPDEs and applications, Stochastic Process, Appl, vol.72, issue.2, pp.161-186, 1997.
DOI : 10.1016/s0304-4149(97)00091-4
URL : http://doi.org/10.1016/s0304-4149(97)00091-4

N. Dunford and J. T. Schwartz, Linear operators. Part I, Wiley Classics Library, 1988.

H. Eyring, The Activated Complex in Chemical Reactions, The Journal of Chemical Physics, vol.3, issue.2, pp.107-115, 1935.
DOI : 10.1063/1.1749604

G. William and G. Faris, Large fluctuations for a nonlinear heat equation with noise, J. Phys. A, vol.15, issue.10, pp.3025-3055, 1982.

R. Forman, Functional determinants and geometry, Inventiones Mathematicae, vol.91, issue.85, pp.447-493, 1987.
DOI : 10.1007/BF01391828

I. Mark and . Freidlin, Random perturbations of reaction-diffusion equations: the quasideterministic approximation, Trans. Amer. Math. Soc, vol.30589, issue.2, pp.665-697, 1988.

M. I. Freidlin and A. D. , Random perturbations of dynamical systems, 1998.

]. Gal93, . Th, and . Gallay, A center-stable manifold theorem for differential equations in Banach spaces, Comm. Math. Phys, vol.152, issue.2, pp.249-268, 1993.

[. Hairer, An introduction to stochastic PDEs, Lecture notes, 2009.

G. Jetschke, On the Equivalence of Different Approaches to Stochastic Partial Differential Equations, Mathematische Nachrichten, vol.13, issue.1, pp.315-329, 1986.
DOI : 10.1002/mana.19861280127

M. S. Jolly, Explicit construction of an inertial manifold for a reaction diffusion equation, Journal of Differential Equations, vol.78, issue.2, pp.220-261, 1989.
DOI : 10.1016/0022-0396(89)90064-8

H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, vol.7, issue.4, pp.284-304, 1940.
DOI : 10.1016/S0031-8914(40)90098-2

D. Liu, Convergence of the Spectral Method for Stochastic Ginzburg-Landau Equation Driven by Space-Time White Noise, Communications in Mathematical Sciences, vol.1, issue.2, pp.361-375, 2003.
DOI : 10.4310/CMS.2003.v1.n2.a9

F. Martinelli, E. Olivieri, and E. Scoppola, Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times, Journal of Statistical Physics, vol.4, issue.4, pp.3-4, 1989.
DOI : 10.1007/BF01041595

S. Robert, D. L. Maier, and . Stein, Droplet nucleation and domain wall motion in a bounded interval, Phys. Rev. Lett, vol.87, pp.270601-270602, 2001.

M. [. Mckane and . Tarlie, Regularization of functional determinants using boundary perturbations, Journal of Physics A: Mathematical and General, vol.28, issue.23, pp.6931-6942, 1995.
DOI : 10.1088/0305-4470/28/23/032

E. Olivieri and M. E. Vares, Large deviations and metastability, Encyclopedia of Mathematics and its Applications, 2005.

S. Saitoh, Weighted L p -norm inequalities in convolutions, Survey on classical inequalities, Math. Appl, vol.517, pp.225-234, 2000.
DOI : 10.1007/978-94-011-4339-4_8

]. D. Ste04 and . Stein, Critical behavior of the Kramers escape rate in asymmetric classical field theories, J. Stat. Phys, vol.114, pp.1537-1556, 2004.

. D. Vf69-]-a and M. I. Ventcel, Fre? ?dlin, Small random perturbations of a dynamical system with stable equilibrium position, Dokl. Akad. Nauk SSSR, vol.187, pp.506-509, 1969.

V. [. Vinokurov and . Sadovnichi?-i, Asymptotics of any order for the eigenvalues and eigenfunctions of the Sturm - Liouville boundary-value problem on a segment with a summable potential, Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, vol.64, issue.4, pp.47-108, 2000.
DOI : 10.4213/im295

B. P. Bâtiment-de-mathématiques, 6759 45067 Orléans Cedex 2, France E-mail address: nils.berglund@univ-orleans