On amenability of automata groups Academic Article

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. 2010.

authors

• Nekrashevych, Volodymyr

published proceedings

• Duke Mathematical Journal

author list (cited authors)

• Bartholdi, L., Kaimanovich, V. A., & Nekrashevych, V. V.

citation count

• 26

complete list of authors

• Bartholdi, Laurent||Kaimanovich, Vadim A||Nekrashevych, Volodymyr V

publication date

• September 2010

publisher

• Duke University Press  Publisher

published in

• DUKE MATHEMATICAL JOURNAL  Journal

keywords

• Math.gr

Digital Object Identifier (DOI)

• 10.1215/00127094-2010-046

start page

• 575

end page

• 598

volume

• 154

issue

• 3

URL

• http://dx.doi.org/10.1215/00127094-2010-046