Non-reversible metastable diffusions with Gibbs invariant measure I: Eyring-Kramers formula

• 成果类型: Article
• 署名作者: Lee, Jungkyoung; Seo, Insuk
• 署名单位: Seoul National University (SNU); Seoul National University (SNU)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01102-z
• 发表日期: 2022
• 页码: 849-903
• 关键词: markov-chains; field; MODEL

摘要

In this article, we prove the Eyring-Kramers formula for non-reversible metastable diffusion processes that have a Gibbs invariant measure. Our result indicates that non-reversible processes exhibit faster metastable transitions between neighborhoods of local minima, compared to the reversible process considered in Bovier et al. (J Eur Math Soc 6:399-424, 2004). Therefore, by adding non-reversibility to the model, we can indeed accelerate the metastable transition. Our proof is based on the potential theoretic approach to metastability through accurate estimation of the capacity between metastable valleys. We carry out this estimation by developing a novel method to compute the sharp asymptotics of the capacity without relying on variational principles such as the Dirichlet principle or the Thomson principle.