Year: 2025
Type: article
Abstract: In this article, we study the mixing properties of metastable diffusion processes which possess a Gibbs invariant distribution. For systems with multiple stable equilibria, so-called metastable transitions between these equilibria are required for mixing since the unique invariant distribution is concentrated on these equilibria. Consequently, these systems exhibit slower mixing compared to those with a unique stable equilibrium, as analyzed in Barrera and Jara (Ann. Appl. Probab. 30:1164–1208, 2020). Our proof is based on the theory of metastability, which is a primary tool for studying systems with multiple stable equilibria. Within this framework, we compute the total variation distance between the distribution of the diffusion process and its invariant distribution for any time scale larger than ϵ−1. Finally, we derive precise asymptotics for the mixing time.
DOI: 10.1214/25-ejp1321
Author: Jungkyoung Lee
Institution: Korea Institute for Advanced Study
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
Awards: G1070282543, G7541485088
OpenAlex ID: W4409305352