Most actions on regular trees are almost free

2008/10/09 by Miklós Abért, Abert, Miklos, Yair Glasner +1 · 1 citation
Mathematics · #05C05 #20E08 #20P05 #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0810.1731

openalex publication_date 2008/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a d-regular tree (d > 2) and A=Aut(T), its automorphism group. Let G be a group generated by n independent Haar-random elements of A. We show that almost surely, every nontrivial element of G has finitely many fixed points on T.

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