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

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

2 Scopus citations

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

Bibliographical note

Funding Information:
We thank Mikael de la Salle for pointing out an imprecision in the statement of Proposition 3.3 in a previous version. GA's research was supported by the Israel Science Foundation (Grant 1471) and by a grant from the GIF, the German-Israeli Foundation for Scientific Research and Development. OA was partially supported by NSERC and ENS in Paris. NMB was introduced to this subject by Anna Erschler, and thanks her for several conversations. The work of NMB was partially supported by the ERC staring Grant GA 257110 "RaWG."

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

Keywords

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

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10.1214/15-AIHP697

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The Liouville property for groups acting on rooted trees

Abstract

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Keywords

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