Self-similarity and random walks

TL;DR

This paper surveys the theory of self-similar groups, focusing on random walks and their applications to understanding the amenability of these groups, providing an introductory overview of this fractal analysis branch.

Contribution

It introduces the concept of self-similar groups and reviews recent research on random walks and amenability within this framework.

Findings

Insights into the behavior of random walks on self-similar groups

Connections between self-similarity and group amenability

Foundational overview for further research in fractal group analysis

Abstract

This is an introductory level survey of some topics from a new branch of fractal analysis -- the theory of self-similar groups. We discuss recent works on random walks on self-similar groups and their applications to the problem of amenability for these groups.