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Uniform estimates for metastable transition times in a coupled bistable system
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Florent Barret, CMAP UMR 7641, École Polytechnique CNRS
Anton Bovier, Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität
Sylvie Méléard, CMAP UMR 7641, École Polytechnique CNRS
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Abstract
We consider a coupled bistable N-particle system on RN
driven by a Brownian noise, with a strong coupling corresponding
to the synchronised regime. Our aim is to obtain sharp estimates
on the metastable transition times between the two stable states,
both for fixed N and in the limit when N tends to infinity,
with error estimates uniform in N. These estimates are a main
step towards a rigorous understanding of the metastable behavior
of infinite dimensional systems, such as the stochastically perturbed
Ginzburg-Landau equation. Our results are based on the potential theoretic approach to metastability.
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Full text: PDF
Pages: 323-345
Published on: April 9, 2010
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Bibliography
-
F. Barret. Metastability: Application to a model of sharp
asymptotics for capacities and exit/hitting times. Master thesis, ENS Cachan (2007).
Math. Review number not available.
-
N. Berglund, B. Fernandez, B. Gentz. Metastability in Interacting Nonlinear Stochastic Differential Equations I: From Weak Coupling to Synchronization.
Nonlinearity 20(11), 2007, 2551-2581.
Math. Review 2009a:60116
-
N. Berglund, B. Fernandez, B. Gentz. Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behavior. Nonlinearity,
20(11), 2007, 2583-2614.
Math. Review 2009a:60117
-
A. Bovier. Metastability, in Methods of
Contemporary Statistical Mechanics (R. Kotecky, ed.), 177-221.
Lecture Notes in Mathematics 1970. Springer, Berlin, 2009.
Math. Review number not available.
-
A. Bovier, M. Eckhoff, V. Gayrard, M. Klein. Metastability in reversible diffusion processes I. Sharp asymptotics for capacities and exit times. Journal of
the European Mathematical Society 6(2), 2004, 399-424.
Math. Review 2006b:82112
-
B. Bianchi, A. Bovier, I. Ioffe. Sharp asymptotics for metastability in the Random Field Curie-Weiss model. Electr. J. Probab. 14 (2008), 1541--1603.
Math. Review MR2525104
-
S. Brassesco. Some results on small random perturbations of an infinite-dimensional dynamical system.
Stochastic Process. Appl. 38 (1991), 33--53.
Math. Review 92k:60125
-
K.L. Chung, J.B. Walsh. Markov processes, Brownian motion, and time symmetry. Second
edition. Springer, 2005.
Math. Review 2006j:60003
-
M.I. Freidlin, A.D. Wentzell. Random Perturbations of Dynamical Systems. Springer, 1984.
Math. Review 99h:60128
-
W.G. Faris, G. Jona-Lasinio. Large fluctuations for a nonlinear heat equation with noise. J. Phys. A 15 (1982),
3025--3055.
Math. Review 84j:81073
-
M. Fukushima, Y. Mashima, M. Takeda. Dirichlet forms and symmetric Markov processes.
de Gruyter Studies in Mathematics 19. Walter de Gruyter & Co., Berlin, 1994.
Math. Review 96f:60126
-
D. Gilbarg, N.S. Trudinger. Elliptic partial differential equations of second order. Springer, 2001.
Math. Review 2001k:35004
-
R. Maier, D. Stein. Droplet nucleation and
domain wall motion in a bounded interval.
Phys. Rev. Lett. 87 (2001), 270601-1--270601-4.
Math. Review number not available.
-
F. Martinelli, E. Olivieri, E. Scoppola. Small random perturbations of
finite- and infinite-dimensional dynamical systems: unpredictability of
exit times. J. Statist. Phys. 55 (1989), 477--504.
Math. Review 91f:60105
-
E. Olivieri, M.E. Vares. Large deviations and metastability.
Encyclopedia of Mathematics and its Applications.
Cambridge University Press, 2005.
Math. Review 2005k:60007
-
M. Reed, B. Simon. Methods of modern mathematical physics:
I Functional Analysis. Second edition. Academic Press, 1980.
Math. Review 85e:46002
-
E. Vanden-Eijnden, M.G. Westdickenberg. Rare events in stochastic partial
differential equations on large spatial domains. J. Stat. Phys. 131 (2008), 1023--1038.
Math. Review 2009d:82053
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Electronic Journal of Probability. ISSN: 1083-6489 |
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