TY - JOUR
T1 - Positive speed for high-degree automaton groups
AU - Amir, Gideon
AU - Virág, Bálint
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Automaton groups
KW - Liouville property
KW - Random walks
UR - http://www.scopus.com/inward/record.url?scp=84900398000&partnerID=8YFLogxK
U2 - 10.4171/GGD/215
DO - 10.4171/GGD/215
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AN - SCOPUS:84900398000
SN - 1661-7207
VL - 8
SP - 23
EP - 38
JO - Groups, Geometry, and Dynamics
JF - Groups, Geometry, and Dynamics
IS - 1
ER -