Most actions on regular trees are almost free

Miklós Abért; Yair Glasner

doi:10.4171/GGD/54

Most actions on regular trees are almost free

Miklós Abért
, Yair Glasner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let T be a d-regular tree (d ≥ 3) and A D Aut(T) its automorphism group. Let Γ be the group generated by n independent Haar-random elements of A. We show that almost surely, every nontrivial element of Γ has finitely many fixed points on T. Mathematics Subject Classification (2000). 20E08, 05C05, 20E05.

Original language	English
Pages (from-to)	199-213
Number of pages	15
Journal	Groups, Geometry, and Dynamics
Volume	3
Issue number	2
DOIs	https://doi.org/10.4171/GGD/54
State	Published - 1 Jan 2009

Keywords

Almost free actions
Dense subgroups
Galton-watson processes
Random generation

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/54

Cite this

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abstract = "Let T be a d-regular tree (d ≥ 3) and A D Aut(T) its automorphism group. Let Γ be the group generated by n independent Haar-random elements of A. We show that almost surely, every nontrivial element of Γ has finitely many fixed points on T. Mathematics Subject Classification (2000). 20E08, 05C05, 20E05.",

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AB - Let T be a d-regular tree (d ≥ 3) and A D Aut(T) its automorphism group. Let Γ be the group generated by n independent Haar-random elements of A. We show that almost surely, every nontrivial element of Γ has finitely many fixed points on T. Mathematics Subject Classification (2000). 20E08, 05C05, 20E05.

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KW - Dense subgroups

KW - Galton-watson processes

KW - Random generation

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Most actions on regular trees are almost free

Abstract

Keywords

ASJC Scopus subject areas

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