JournalsggdVol. 3 , No. 2DOI 10.4171/ggd/54

Most actions on regular trees are almost free

  • Miklós Abért

    Hungarian Academy of Sciences, Budapest, Hungary
  • Yair Glasner

    Ben Gurion University of the Negev, Beer Sheva, Israel
Most actions on regular trees are almost free cover

Abstract

Let T be a d-regular tree (d ≥ 3) and A = 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.