Percolation in acylindrically hyperbolic groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909735171653632 |
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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 |