Formulas for Hitting Times and Cover Times for Random Walks on Groups

TL;DR

This paper develops explicit formulas for calculating hitting and cover times of random walks on groups, utilizing group representations and a novel volume growth function to deepen understanding of these stochastic processes.

Contribution

It introduces explicit formulas for hitting and cover times on groups based on irreducible representations and a new volume growth function, advancing theoretical understanding.

Findings

Derived explicit formulas for hitting times using group representations

Connected cover times to a new volume growth function

Provided a framework for analyzing random walks on groups

Abstract

Using the results of Ding, Lee, Peres [3], we develop formulas to compute the hitting times and cover times for random walks on groups. We developed an explicit formula for hitting times in terms of the irreducible representations of the group. We also have a way of computing cover times in terms of these hitting times. This computation is based on a quantity we indentified, which we call the volume growth function. And we believe that it is the right object to study in order to understand the cover time.