Most actions on regular trees are almost free

Miklós Abért, Yair Glasner

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)199-213
Number of pages15
JournalGroups, Geometry, and Dynamics
Volume3
Issue number2
DOIs
StatePublished - 1 Jan 2009

Keywords

  • Almost free actions
  • Dense subgroups
  • Galton-watson processes
  • Random generation

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