Positive speed for high-degree automaton groups

Gideon Amir; Bálint Virág

doi:https://doi.org/10.4171/GGD/215

Positive speed for high-degree automaton groups

Gideon Amir, Bálint Virág

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	23-38
Number of pages	16
Journal	Groups, Geometry, and Dynamics
Volume	8
Issue number	1
DOIs	https://doi.org/10.4171/GGD/215
State	Published - 2014

Keywords

Automaton groups
Liouville property
Random walks

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

https://doi.org/10.4171/GGD/215

Cite this

@article{b265bb03b1d7458b8f02dc02260118d6,

title = "Positive speed for high-degree automaton groups",

abstract = "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.",

keywords = "Automaton groups, Liouville property, Random walks",

author = "Gideon Amir and B{\'a}lint Vir{\'a}g",

year = "2014",

doi = "https://doi.org/10.4171/GGD/215",

language = "الإنجليزيّة",

volume = "8",

pages = "23--38",

journal = "Groups, Geometry, and Dynamics",

issn = "1661-7207",

publisher = "European Mathematical Society Publishing House",

number = "1",

}

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 - https://doi.org/10.4171/GGD/215

DO - https://doi.org/10.4171/GGD/215

M3 - مقالة

SN - 1661-7207

VL - 8

SP - 23

EP - 38

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 1

ER -

Positive speed for high-degree automaton groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this