Percolation in acylindrically hyperbolic groups

Abstract

Let $G$ be an acylindrically hyperbolic group. We prove that Bernoulli bond percolation on every Cayley graph of $G$ has a nonuniqueness phase, in which there are infinitely many infinite clusters. This generalizes Hutchcroft's result for Gromov hyperbolic graphs to relatively hyperbolic groups, mapping class groups and rank-1 CAT(0) groups for example.

arXiv comment61 pages, 3 figures. v2: corrected some references and typos. Comments are welcome