# Amenability of linear-activity automaton groups

Gideon Amir; Omer Angel; Bálint Virág

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 3, page 705-730
- ISSN: 1435-9855

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topAmir, 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 -

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