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

This article considers a class of metastable non-reversible diffusion processes whose invariant measure is Gibbs associated with Morse potential. In companion paper (Lee and Seo in Probab Theory Relat Fields 182:849–903, 2022), we proved the Eyring–Kramers formula for corresponding processes. this article, further develop result by proving that suitably time-rescaled process converges to Markov chain on deepest valleys. also an extension (Rezakhanlou https://arxiv.org/abs/1812.02069 , 2018), which considered same problem reversible Our proof based recently developed resolvent approach metastability.