Geodesic
Amenability of linear-activity automaton groups
Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 705-730

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/373
Classification : 60-XX, 20-XX, 00-XX
Keywords: amenability, automaton groups, self-similar, random walk, entropy 
@article{JEMS_2013_15_3_a0,
     author = {Gideon Amir and Omer Angel and B\'alint Vir\'ag},
     title = {Amenability of linear-activity automaton groups},
     journal = {Journal of the European Mathematical Society},
     pages = {705--730},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2013},
     doi = {10.4171/jems/373},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/373/}
}
TY  - JOUR
AU  - Gideon Amir
AU  - Omer Angel
AU  - Bálint Virág
TI  - Amenability of linear-activity automaton groups
JO  - Journal of the European Mathematical Society
PY  - 2013
SP  - 705
EP  - 730
VL  - 15
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/373/
DO  - 10.4171/jems/373
ID  - JEMS_2013_15_3_a0
ER  - 
%0 Journal Article
%A Gideon Amir
%A Omer Angel
%A Bálint Virág
%T Amenability of linear-activity automaton groups
%J Journal of the European Mathematical Society
%D 2013
%P 705-730
%V 15
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/373/
%R 10.4171/jems/373
%F JEMS_2013_15_3_a0
Gideon Amir; Omer Angel; Bálint Virág. Amenability of linear-activity automaton groups. Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 705-730. doi: 10.4171/jems/373

Cité par Sources :