The Liouville property for groups acting on rooted trees

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

Research output: Contribution to journalArticlepeer-review

3 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 languageEnglish
Pages (from-to)1763-1783
Number of pages21
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume52
Issue number4
DOIs
StatePublished - Nov 2016

Bibliographical note

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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