论文标题
限制可逆的马尔可夫连锁店的轮廓
Limit Profiles for Reversible Markov Chains
论文作者
论文摘要
在最近的突破中，Teysier [TEY20]引入了一种新方法，用于近似于一组随机行走的距离。他用它来研究随机换位卡的限制轮廓。他的技术仅限于在小组上随机步行。我们为在同质空间和一般可逆的马尔可夫连锁店上随机行走而得出相似的近似引理。我们将这些引理的应用说明在一些著名的问题中：$ K $ cycleShuffle，改善Hough [Hou16]和Berestycki，Schramm和Zeitouni [BSZ11]的结果； Ehrenfest urn扩散有许多urn，改善了Ceccherini-Silberstein，Scarabotti和Tolli的结果[CST07]； Gibbs Sampler是统计物理学中的基本工具，具有二项式先验和过度几何后部，可改善Diaconis，Khare和Saloff-Coste的结果[DKS08]。
In a recent breakthrough, Teyssier [Tey20] 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, improving results of Hough [Hou16] and Berestycki, Schramm and Zeitouni [BSZ11]; the Ehrenfest urn diffusion with many urns, improving results of Ceccherini-Silberstein, Scarabotti and Tolli [CST07]; a Gibbs sampler, which is a fundamental tool in statistical physics, with Binomial prior and hypergeometric posterior, improving results of Diaconis, Khare and Saloff-Coste [DKS08].
