On amenability of automata groups
Group Theory
2019-12-19 v1
Abstract
We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability just of a certain explicit family of groups ("Mother groups") which is done by analyzing the asymptotic properties of random walks on these groups.
Cite
@article{arxiv.0802.2837,
title = {On amenability of automata groups},
author = {Laurent Bartholdi and Vadim A. Kaimanovich and Volodymyr V. Nekrashevych},
journal= {arXiv preprint arXiv:0802.2837},
year = {2019}
}