发表机构
Shizuoka University（静冈大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为有限马尔可夫链建立无需对称支撑条件的割断判据，推广了Salez的结果，并应用于有限阿贝尔群上的随机游走，证明其几乎必然割断。
AI 中文摘要
我们为具有非负 Bakry--Émery 曲率的有限马尔可夫链建立了割断判据，且不要求转移矩阵的支撑集是对称的。这推广了 Salez 基于精细乘积条件的判据。对于每个允许的转移，我们考虑一条从终点回到起点的最短有向路径。我们的割断判据依赖于这些路径的最大长度。我们还为懒惰链获得了离散时间版本的对应结果。对于有限阿贝尔群上的随机游走，我们证明了任意生成集都具有非负 Bakry--Émery 曲率。作为应用，我们建立了三阶循环群乘积上随机游走的几乎必然割断现象。
英文摘要
We establish a cutoff criterion for finite Markov chains with non-negative Bakry--Émery curvature without assuming that the support of the transition matrix is symmetric. This extends a criterion of Salez based on a refined product condition. For each allowed transition, we consider a shortest directed path from its endpoint back to its starting point. Our cutoff criterion depends on the maximum length of these paths. We also obtain a discrete-time counterpart for lazy chains. For random walks on finite Abelian groups, we prove non-negative Bakry--Émery curvature for arbitrary generating sets. As an application, we establish almost-sure cutoff for random walks on products of cyclic groups of order three.
Comments27 pages
