The CLT for lamplighter groups with an acylindrically hyperbolic base
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911251288817664 |
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| author | Chaudkhari, Maksym Gorski, Christian Silva, Eduardo |
| author_facet | Chaudkhari, Maksym Gorski, Christian Silva, Eduardo |
| contents | We prove a Central Limit Theorem for the drift of a non-elementary random walk with a finite exponential moment on a wreath product $A\wr H=\bigoplus_{H} A\rtimes H$ with $A$ a non-trivial finite group and $H$ a finitely generated acylindrically hyperbolic group. We also provide the upper bounds on the central moments of the drift. Furthermore, our results extend to the case where $A$ is an arbitrary (possibly infinite) finitely generated group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The CLT for lamplighter groups with an acylindrically hyperbolic base Chaudkhari, Maksym Gorski, Christian Silva, Eduardo Probability Group Theory We prove a Central Limit Theorem for the drift of a non-elementary random walk with a finite exponential moment on a wreath product $A\wr H=\bigoplus_{H} A\rtimes H$ with $A$ a non-trivial finite group and $H$ a finitely generated acylindrically hyperbolic group. We also provide the upper bounds on the central moments of the drift. Furthermore, our results extend to the case where $A$ is an arbitrary (possibly infinite) finitely generated group. |
| title | The CLT for lamplighter groups with an acylindrically hyperbolic base |
| topic | Probability Group Theory |
| url | https://arxiv.org/abs/2511.04241 |