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arXiv:1307.5652 [math.GR]AbstractReferencesReviewsResources

The Liouville property for groups acting on rooted trees

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

Published 2013-07-22, updated 2015-07-09Version 2

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.

Comments: Major changes in the statement and proof of Theorem 1, it now holds for all groups of automorphisms of bounded type, not necessarily finite-state. Final version, to appear in Annales de l'IHP
Categories: math.GR, math.PR
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