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arXiv · 2508.08932

Percolation in acylindrically hyperbolic groups

Inhyeok Choi·Donggyun Seo
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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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Inhyeok Choi, Donggyun Seo. 2025-08-12. Percolation in acylindrically hyperbolic groups. https://arxiv.org/abs/2508.08932

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