%0 Journal Article
%T On amenability of automata groups
%A Laurent Bartholdi
%A Vadim A. Kaimanovich
%A Volodymyr V. Nekrashevych
%J Mathematics
%D 2008
%I arXiv
%R 10.1215/00127094-2010-046
%X 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.
%U http://arxiv.org/abs/0802.2837v1