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.
Classification :
20-XX, 05-XX, 00-XX
Mots-clés :
Random generation, almost free actions, dense subgroups, Galton–Watson processes
Affiliations des auteurs :
Miklós Abért
1
;
Yair Glasner
2
1
Hungarian Academy of Sciences, Budapest, Hungary
2
Ben Gurion University of the Negev, Beer Sheva, Israel
Miklós Abért; Yair Glasner. Most actions on regular trees are almost free. Groups, geometry, and dynamics, Tome 3 (2009) no. 2, pp. 199-213. doi: 10.4171/ggd/54
@article{10_4171_ggd_54,
author = {Mikl\'os Ab\'ert and Yair Glasner},
title = {Most actions on regular trees are almost free},
journal = {Groups, geometry, and dynamics},
pages = {199--213},
year = {2009},
volume = {3},
number = {2},
doi = {10.4171/ggd/54},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/54/}
}
TY - JOUR
AU - Miklós Abért
AU - Yair Glasner
TI - Most actions on regular trees are almost free
JO - Groups, geometry, and dynamics
PY - 2009
SP - 199
EP - 213
VL - 3
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/54/
DO - 10.4171/ggd/54
ID - 10_4171_ggd_54
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%A Yair Glasner
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%J Groups, geometry, and dynamics
%D 2009
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/54/
%R 10.4171/ggd/54
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