论文标题
与吉布斯不变的度量II：马尔可夫链收敛的非可逆亚稳态扩散
Non-reversible Metastable Diffusions with Gibbs Invariant Measure II: Markov Chain Convergence
论文作者
论文摘要
本文考虑了一类亚稳态的非可逆扩散过程，其不变的度量是与摩尔斯电位相关的吉布斯度量。在伴侣论文[32]中，我们证明了相应的亚稳态扩散过程的眼环式公式。在本文中，我们通过证明适当的时间响应的亚稳定扩散过程将其进一步发展为最深的亚稳态谷上的马尔可夫链。本文也是[45]的扩展，它考虑了亚稳态可逆扩散过程的相同问题。我们的证明是基于最近开发的分解方法来稳定性的。
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.
