Amenability of linear-activity automaton groups

Amir, Gideon, Angel, Omer, and Virág, Bálint. "Amenability of linear-activity automaton groups." Journal of the European Mathematical Society 015.3 (2013): 705-730. <http://eudml.org/doc/277531>.

@article{Amir2013,
abstract = {We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.},
author = {Amir, Gideon, Angel, Omer, Virág, Bálint},
journal = {Journal of the European Mathematical Society},
keywords = {amenability; automaton groups; self-similar; random walk; entropy; amenability; automaton groups; self-similar; random walk; entropy},
language = {eng},
number = {3},
pages = {705-730},
publisher = {European Mathematical Society Publishing House},
title = {Amenability of linear-activity automaton groups},
url = {http://eudml.org/doc/277531},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Amir, Gideon
AU - Angel, Omer
AU - Virág, Bálint
TI - Amenability of linear-activity automaton groups
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 3
SP - 705
EP - 730
AB - We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
LA - eng
KW - amenability; automaton groups; self-similar; random walk; entropy; amenability; automaton groups; self-similar; random walk; entropy
UR - http://eudml.org/doc/277531
ER -