Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
Random walks and quasi-convexity in acylindrically hyperbolic groups Journal of Topology (IF1.582), Pub Date : 2021-09-29, DOI: 10.1112/topo.12205 Carolyn Abbott, Michael Hull
Arzhantseva proved that every infinite-index quasi-convex subgroup of a torsion-free hyperbolic group is a free factor in a larger quasi-convex subgroup of . We give a probabilistic generalization of this result. That is, we show that when is a subgroup generated by independent random walks in , then with probability going to one as the lengths of the random walks go to infinity and this subgroup is quasi-convex in . Moreover, our results hold for a large class of groups acting on hyperbolic metric spaces and subgroups with quasi-convex orbits. In particular, when is the mapping class group of a surface and is a convex cocompact subgroup we show that is convex cocompact and isomorphic to .