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

Abstract

We consider non-reversible random walks evolving on a potential field in a bounded domain of ${\mathbb{R}}^d$. We describe the complete metastable behavior of the random walk among the landscape of valleys, and we derive the Eyring-Kramers formula for the mean transition time from a metastable set to a stable set.

53 pages, 6 figures

References in corpus (2)

• Dirichlet's and Thomson's principles for non-selfadjoint elliptic operators with application to non-reversible metastable diffusion processes
• Metastability of the two-dimensional Blume-Capel model with zero chemical potential and small magnetic field

Cited by in corpus (6)

• Generalisation of the Eyring-Kramers transition rate formula to irreversible diffusion processes
• Dirichlet's and Thomson's principles for non-selfadjoint elliptic operators with application to non-reversible metastable diffusion processes
• Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions
• Energy Landscape and Metastability of Curie-Weis-Potts Model
• Metastability of one-dimensional, non-reversible diffusions with periodic boundary conditions
• Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions