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.
@article{10_4171_ggd_215,
author = {Gideon Amir and B\'alint Vir\'ag},
title = {Positive speed for high-degree automaton groups},
journal = {Groups, geometry, and dynamics},
pages = {23--38},
year = {2014},
volume = {8},
number = {1},
doi = {10.4171/ggd/215},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/215/}
}
TY - JOUR
AU - Gideon Amir
AU - Bálint Virág
TI - Positive speed for high-degree automaton groups
JO - Groups, geometry, and dynamics
PY - 2014
SP - 23
EP - 38
VL - 8
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/215/
DO - 10.4171/ggd/215
ID - 10_4171_ggd_215
ER -
%0 Journal Article
%A Gideon Amir
%A Bálint Virág
%T Positive speed for high-degree automaton groups
%J Groups, geometry, and dynamics
%D 2014
%P 23-38
%V 8
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/215/
%R 10.4171/ggd/215
%F 10_4171_ggd_215
