Metastability of one-dimensional, non-reversible diffusions with periodic boundary conditions
Probability
2017-10-19 v1 Statistical Mechanics
Abstract
We consider small perturbations of a dynamical system on the one-dimensional torus. We derive sharp estimates for the pre-factor of the stationary state, we examine the asymptotic behavior of the solutions of the Hamilton-Jacobi equation for the pre-factor, we compute the capacities between disjoint sets, and we prove the metastable behavior of the process among the deepest wells following the martingale approach. We also present a bound for the probability that a Markov process hits a set before some fixed time in terms of the capacity of an enlarged process.
Keywords
Cite
@article{arxiv.1710.06672,
title = {Metastability of one-dimensional, non-reversible diffusions with periodic boundary conditions},
author = {C. Landim and I. Seo},
journal= {arXiv preprint arXiv:1710.06672},
year = {2017}
}