Non-reversible Metastable Diffusions with Gibbs Invariant Measure II: Markov Chain Convergence

Abstract

This article considers a class of metastable non-reversible diffusion processes whose invariant measure is a Gibbs measure associated with a Morse potential. In a companion paper [32], we proved the Eyring-Kramers formula for the corresponding class of metastable diffusion processes. In this article, we further develop this result by proving that a suitably time-rescaled metastable diffusion process converges to a Markov chain on the deepest metastable valleys. This article is also an extension of [45], which considered the same problem for metastable reversible diffusion processes. Our proof is based on the recently developed resolvent approach to metastability.

39 pages, 4 figures (the article is significantly revised at 2022-07-20; the resolvent approach is used to simplify the argument)

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