Mixing time bounds via bottleneck sequences

TL;DR

This paper introduces new upper bounds for the mixing times of finite Markov chains and demonstrates their robustness under rough isometry for certain graph classes, enhancing understanding of Markov chain convergence.

Contribution

The paper presents novel upper bounds on mixing times and establishes their robustness under rough isometry for bounded degree graphs roughly isometric to trees.

Findings

New upper bounds for mixing times of finite Markov chains.

Robustness of total variation mixing time under rough isometry.

Applicability to graphs roughly isometric to trees.

Abstract

We provide new upper bounds for mixing times of general finite Markov chains. We use these bounds to show that the total variation mixing time is robust under rough isometry for bounded degree graphs that are roughly isometric to trees.