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.
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