Groups, Geometry, and Dynamics

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Volume 3, Issue 2, 2009, pp. 199–213
DOI: 10.4171/GGD/54

Published online: 2009-06-30

Most actions on regular trees are almost free

Miklós Abért[1] and Yair Glasner[2]

(1) Hungarian Academy of Sciences, Budapest, Hungary
(2) Ben Gurion University of the Negev, Beer Sheva, Israel

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.

Keywords: Random generation, almost free actions, dense subgroups, Galton–Watson processes

Abért Miklós, Glasner Yair: Most actions on regular trees are almost free. Groups Geom. Dyn. 3 (2009), 199-213. doi: 10.4171/GGD/54