Uniform Estimates for Metastable Transition times in a Coupled Bistable System

We consider a coupled bistable N -particle system on R 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 betwen the two stable states, both for fixed N and in the limit when N tends to infinity. These estimates would be the main step for a rigorous understanding of the metastable behavior of infinite dimensional systems, as the stochastically perturbed GinzburgLandau equation. The quantities of interest are objects of potential theory, as capacities and equilibrium measure. We prove estimates with error bounds that are uniform in the dimension of the system. MSC 2000 subject classification: 82C44, 60K35. Key-words: Metastability, Coupled bistable systems, Metastable transition time, Capacity estimates.