Electronic Journal of Probability

Uniform Estimates for Metastable Transition Times in a Coupled Bistable System

Florent Barret, Anton Bovier, and Sylvie Méléard

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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.

Article information

Electron. J. Probab., Volume 15 (2010), paper no. 12, 323-345.

Accepted: 9 April 2010
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82C44: Dynamics of disordered systems (random Ising systems, etc.)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Metastability coupled bistable systems stochastic Ginzburg-Landau equation metastable transition time capacity estimates

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Barret, Florent; Bovier, Anton; Méléard, Sylvie. Uniform Estimates for Metastable Transition Times in a Coupled Bistable System. Electron. J. Probab. 15 (2010), paper no. 12, 323--345. doi:10.1214/EJP.v15-751. https://projecteuclid.org/euclid.ejp/1464819797

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