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.
Publié le : 2010-09-15
Classification:
20E08,
20P05,
37A50,
43A07,
60G50
@article{1283865313,
author = {Bartholdi, Laurent and Kaimanovich, Vadim A. and Nekrashevych, Volodymyr V.},
title = {On amenability of automata groups},
journal = {Duke Math. J.},
volume = {151},
number = {1},
year = {2010},
pages = { 575-598},
language = {en},
url = {http://dml.mathdoc.fr/item/1283865313}
}
Bartholdi, Laurent; Kaimanovich, Vadim A.; Nekrashevych, Volodymyr V. On amenability of automata groups. Duke Math. J., Tome 151 (2010) no. 1, pp. 575-598. http://gdmltest.u-ga.fr/item/1283865313/