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arXiv · 2008.08295

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

Jungkyoung Lee·Insuk Seo
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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.

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Jungkyoung Lee, Insuk Seo. 2020-08-19. Non-reversible Metastable Diffusions with Gibbs Invariant Measure II: Markov Chain Convergence. https://arxiv.org/abs/2008.08295

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