SPECTRAL GAP AND CURVATURE OF MONOTONE MARKOV CHAINS

• 成果类型: Article
• 署名作者: Salez, Justin
• 署名单位: Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1688
• 发表日期: 2024
• 页码: 1153-1161
• 关键词: mixing times; inequalities; walk

摘要

We prove that the absolute spectral gap of any monotone Markov chain coincides with its optimal Ollivier-Ricci curvature, where the word optimal refers to the choice of the underlying metric. Moreover, we provide a new expression in terms of local variations of increasing functions, which has several practical advantages over the traditional variational formulation using the Dirichlet form. As an illustration, we explicitly determine the optimal curvature and spectral gap of the nonconservative exclusion process with heterogeneous reservoir densities on any network, despite the lack of reversibility.