Metastability of one-dimensional, non-reversible diffusions with periodic boundary conditions

2017/10/18 by Cláudio Landim, Landim, C., Il Won Seo +1
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1710.06672

openalex publication_date 2017/10/18 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

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.

Citations

• Metastability of non-reversible random walks in a potential field, the Eyring-Kramers transition rate formula

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