Work

On amenability of automata groups

Year: 2010

Type: 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.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2010-046

Authors: Laurent Bartholdi, Vadim A. Kaimanovich, Volodymyr V. Nekrashevych

Institutions: University of Göttingen, University of Ottawa, Texas A&M University

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2047119136

FWCI: 3.094

Cites: 26

Cited by: 53

Related to: 10