AMENABILITY OF AUTOMATA GROUPS
Laurent Bartholdi, Vadim A. Kaimanovich, Volodymyr Nekrashevych · 2008
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.