Uniform estimates for metastable transition times in a coupled bistable system
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
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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