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

2302.01963Feb 3, 2023This is old work from 2017 that I never intended to publish, but it has been on my website for a number of years. I'm adding it to arXiv at the request of others who would like to cite it. Unfortunately the original tex source code has been lost long ago, so I am not able to make any corrections to it. I apologize for any errors

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

Christopher Zhang

Probability

arXiv PDF

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.

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