Limit profiles for reversible Markov chains

• 成果类型: Article
• 署名作者: Nestoridi, Evita; Olesker-Taylor, Sam
• 署名单位: Princeton University; University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01061-5
• 发表日期: 2022
• 页码: 157-188
• 关键词: random-walks; finite-groups; cutoff; permutation

摘要

In a recent breakthrough, Teyssier (Ann Probab 48(5):2323-2343, 2020) introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacy-invariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous spaces and for general reversible Markov chains. We illustrate applications of these lemmas to some famous problems: the k-cycle shuffle, sharpening results of Hough (Probab Theory Relat Fields 165(1-2):447-482, 2016) and Berestycki, Schramm and Zeitouni (Ann Probab 39(5):1815-1843, 2011), the Ehrenfest urn diffusion with many urns, sharpening results of Ceccherini-Silberstein, Scarabotti and Tolli (J Math Sci 141(2):1182-1229, 2007), a Gibbs sampler, which is a fundamental tool in statistical physics, with Binomial prior and hypergeometric posterior, sharpening results of Diaconis, Khare and Saloff-Coste (Stat Sci 23(2):151-178, 2008).