Percolation in acylindrically hyperbolic groups
Group Theory
2025-08-14 v2 Geometric Topology
Probability
Abstract
Let be an acylindrically hyperbolic group. We prove that Bernoulli bond percolation on every Cayley graph of 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.
Cite
@article{arxiv.2508.08932,
title = {Percolation in acylindrically hyperbolic groups},
author = {Inhyeok Choi and Donggyun Seo},
journal= {arXiv preprint arXiv:2508.08932},
year = {2025}
}
Comments
61 pages, 3 figures. v2: corrected some references and typos. Comments are welcome