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arXiv · 1307.5652

The Liouville property for groups acting on rooted trees

Gideon Amir·Omer Angel·Nicolás Matte Bon·Bálint Virág
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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.

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Gideon Amir, Omer Angel, Nicolás Matte Bon, Bálint Virág. 2015-07-09. The Liouville property for groups acting on rooted trees. https://doi.org/10.1214/15-aihp697

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