Percolation in acylindrically hyperbolic groups

Fuente: arXiv
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Main Authors: Choi, Inhyeok, Seo, Donggyun
Format: Preprint
Published: 2025
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author Choi, Inhyeok
Seo, Donggyun
author_facet Choi, Inhyeok
Seo, Donggyun
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_08932
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Percolation in acylindrically hyperbolic groups
Choi, Inhyeok
Seo, Donggyun
Group Theory
Geometric Topology
Probability
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.
title Percolation in acylindrically hyperbolic groups
topic Group Theory
Geometric Topology
Probability
url https://arxiv.org/abs/2508.08932