Uniform Estimates for Metastable Transition Times in a Coupled Bistable System

Florent Barret (École Polytechnique)
Anton Bovier (Rheinische Friedrich-Wilhelms-Universität)
Sylvie Méléard (École Polytechnique)


We consider a coupled bistable $N$-particle system on $\mathbb{R}^N$ 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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Pages: 323-345

Publication Date: April 9, 2010

DOI: 10.1214/EJP.v15-751


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