- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:00
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
8
2014
1
Positive speed for high-degree automaton groups
Gideon
Amir
Bar-Ilan University, RAMAT GAN, ISRAEL
Bálint
Virág
University of Toronto, TORONTO, ONTARIO, CANADA
Automaton groups, random walks, Liouville property
Mother groups are the basic building blocks for polynomial automaton groups. We show that, in contrast with mother groups of degree 0 or 1, any bounded, symmetric, generating random walk on the mother groups of degree at least 3 has positive speed. The proof is based on an analysis of resistance in fractal mother graphs. We give upper bounds on resistances in these graphs, and show that infinite versions are transient.
Probability theory and stochastic processes
23
38
10.4171/GGD/215
http://www.ems-ph.org/doi/10.4171/GGD/215