Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings
Geometric Topology
2017-01-03 v1 Group Theory
Probability
Abstract
Let G be an acylindrically hyperbolic group. We consider a random subgroup H in G, generated by a finite collection of independent random walks. We show that, with asymptotic probability one, such a random subgroup H of G is a free group, and the semidirect product of H acting on E(G) is hyperbolically embedded in G, where E(G) is the unique maximal finite normal subgroup of G.
Cite
@article{arxiv.1701.00253,
title = {Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings},
author = {Joseph Maher and Alessandro Sisto},
journal= {arXiv preprint arXiv:1701.00253},
year = {2017}
}