Uniform estimates for metastable transition times in a coupled bistable system

TL;DR

This paper provides uniform estimates for the transition times between stable states in a coupled N-particle bistable system driven by noise, advancing understanding of metastability in both finite and infinite dimensions.

Contribution

It offers sharp, uniform-in-N estimates for metastable transition times in a coupled bistable system, bridging finite and infinite-dimensional analysis.

Findings

Sharp estimates on transition times obtained

Uniform error bounds in N established

Results applicable to infinite-dimensional systems like Ginzburg-Landau

Abstract

We consider a coupled bistable N-particle system 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.