The Liouville property for groups acting on rooted trees
| Autor: | Nicolás Matte Bon, Omer Angel, Gideon Amir, Bálint Virág |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
20E08 05C81 010102 general mathematics Probability (math.PR) 20F69 Group Theory (math.GR) 16. Peace & justice 01 natural sciences Random walk entropy 010104 statistics & probability Groups acting on rooted trees FOS: Mathematics Liouville property 0101 mathematics Statistics Probability and Uncertainty Recurrent Schreier graphs Humanities Mathematics - Group Theory Mathematics - Probability Mathematics |
| Zdroj: | Ann. Inst. H. Poincaré Probab. Statist. 52, no. 4 (2016), 1763-1783 |
| Popis: | 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. Comment: 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 |
| Databáze: | OpenAIRE |
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