Transformations of random walks on groups via Markov stopping times

TL;DR

This paper introduces a novel method for constructing measures on groups that preserve the Poisson boundary by applying Markov stopping times to extended random walks, offering new insights into the structure of random walks on groups.

Contribution

It presents a new construction technique using Markov stopping times to generate measures with the same Poisson boundary on groups, expanding the toolkit for analyzing random walks.

Findings

Measures with identical Poisson boundaries constructed via stopping times

Extension of random walks preserves boundary properties

New approach broadens understanding of random walk transformations

Abstract

We describe a new construction of a family of measures on a group with the same Poisson boundary. Our approach is based on applying Markov stopping times to an extension of the original random walk.