Exit time for anchored expansion

TL;DR

This paper establishes upper bounds on the exit and occupation times of reversible random walks on graphs with anchored isoperimetric inequalities, with applications to random environments in d.

Contribution

It provides new bounds for exit times of random walks on graphs satisfying anchored isoperimetric inequalities, extending understanding of their behavior in complex environments.

Findings

Upper bounds for exit times of random walks

Application to random environments in d

Insights into occupation times in transient cases

Abstract

Let $(X_n)_{n\geq 0}$ be a reversible random walk on a graph $G$ satisfying an anchored isoperimetric inequality. We give upper bounds for exit time (and occupation time in transient case) by X of any set which contains the root. As an application, we consider random environments of $\Z^d$.