TY - JOUR
T1 - The boundary action of a sofic random subgroup of the free group
AU - Cannizzo, Jan
N1 - Publisher Copyright:
© European Mathematical Society.
PY - 2015
Y1 - 2015
N2 - We prove that the boundary action of a sofic random subgroup of a finitely generated free group is conservative (there are no wandering sets). This 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 sofic 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 sofic random Schreier graph.
AB - We prove that the boundary action of a sofic random subgroup of a finitely generated free group is conservative (there are no wandering sets). This 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 sofic 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 sofic random Schreier graph.
KW - Conservativity
KW - Invariant random subgroups
KW - Schreier graphs
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U2 - 10.4171/GGD/324
DO - 10.4171/GGD/324
M3 - Article
AN - SCOPUS:84969866305
SN - 1661-7207
VL - 9
SP - 683
EP - 709
JO - Groups, Geometry, and Dynamics
JF - Groups, Geometry, and Dynamics
IS - 3
ER -