- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
9
2015
3
The boundary action of a sofic random subgroup of the free group
Jan
Cannizzo
Stevens Institute of Technology, HOBOKEN, UNITED STATES
Invariant random subgroups, Schreier graphs, conservativity
We prove that the boundary action of a sofi c random subgroup of a finitely generated free group is conservative (there are no wandering sets). Th is addresses a question asked by Grigorchuk, Kaimanovich, and Nagnibeda, who studied the boundary actions of individual subgroups of the free group. We also investigate the cogrowth and various limit sets associated to so fic random subgroups. We make heavy use of the correspondence between subgroups and their Schreier graphs, and central to our approach is an investigation of the asymptotic density of a given set inside of large neighborhoods of the root of a so fic random Schreier graph.
Dynamical systems and ergodic theory
Group theory and generalizations
683
709
10.4171/GGD/324
http://www.ems-ph.org/doi/10.4171/GGD/324