The Liouville property for groups acting on rooted trees

Gideon Amir; Omer Angel; Nicolás Matte Bon; Bálint Virág

doi:10.1214/15-AIHP697

The Liouville property for groups acting on rooted trees

Gideon Amir
, Omer Angel
, Nicolás Matte Bon
, Bálint Virág

Department of Mathematics

Bar-Ilan University

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

Abstract

We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted tree. For automaton groups, we also give a uniform upper bound for the entropy of convolutions of every symmetric, finitely supported measure.

Original language	English
Pages (from-to)	1763-1783
Number of pages	21
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	52
Issue number	4
DOIs	https://doi.org/10.1214/15-AIHP697
State	Published - Nov 2016

Keywords

Groups acting on rooted trees
Liouville property
Random walk entropy
Recurrent Schreier graphs

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/15-AIHP697

Cite this

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title = "The Liouville property for groups acting on rooted trees",

abstract = "We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted tree. For automaton groups, we also give a uniform upper bound for the entropy of convolutions of every symmetric, finitely supported measure.",

keywords = "Groups acting on rooted trees, Liouville property, Random walk entropy, Recurrent Schreier graphs",

author = "Gideon Amir and Omer Angel and Bon, \{Nicol{\'a}s Matte\} and B{\'a}lint Vir{\'a}g",

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AU - Amir, Gideon

AU - Angel, Omer

AU - Bon, Nicolás Matte

AU - Virág, Bálint

N1 - Publisher Copyright: © Association des Publications de l'Institut Henri Poincaré, 2016.

PY - 2016/11

Y1 - 2016/11

N2 - We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted tree. For automaton groups, we also give a uniform upper bound for the entropy of convolutions of every symmetric, finitely supported measure.

AB - We show that on groups generated by bounded activity automata, every symmetric, finitely supported probability measure has the Liouville property. More generally we show this for every group of automorphisms of bounded type of a rooted tree. For automaton groups, we also give a uniform upper bound for the entropy of convolutions of every symmetric, finitely supported measure.

KW - Groups acting on rooted trees

KW - Liouville property

KW - Random walk entropy

KW - Recurrent Schreier graphs

UR - https://www.scopus.com/pages/publications/84997235801

U2 - 10.1214/15-AIHP697

DO - 10.1214/15-AIHP697

M3 - مقالة

SN - 0246-0203

VL - 52

SP - 1763

EP - 1783

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 4

ER -

The Liouville property for groups acting on rooted trees

Abstract

Keywords

ASJC Scopus subject areas

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