Sharp asymptotics of metastable transition times for one dimensional SPDEs

TL;DR

This paper derives precise asymptotics for transition times between metastable states in 1D stochastic PDEs, extending the Eyring-Kramers formula to infinite dimensions using finite difference discretization.

Contribution

It establishes a version of the Eyring-Kramers formula for infinite-dimensional SPDEs and provides uniform control of transition times in finite-dimensional approximations.

Findings

Derived asymptotics for transition times in 1D SPDEs

Proved an infinite-dimensional Eyring-Kramers formula

Controlled approximation errors uniformly in dimension

Abstract

We consider a class of parabolic semi-linear stochastic partial differential equations driven by space-time white noise on a compact space interval. Our aim is to obtain precise asymptotics of the transition times between metastable states. A version of the so-called Eyring-Kramers Formula is proven in an infinite dimensional setting. The proof is based on a spatial finite difference discretization of the stochastic partial differential equation. The expected transition time is computed for the finite dimensional approximation and controlled uniformly in the dimension.