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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2307.08878 |
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| _version_ | 1866929656045764608 |
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| author | Silva, Eduardo |
| author_facet | Silva, Eduardo |
| contents | We study random walks on the lampshuffler group $\mathrm{FSym}(H)\rtimes H$, where $H$ is a finitely generated group and $\mathrm{FSym}(H)$ is the group of finitary permutations of $H$. We show that for any step distribution $μ$ with a finite first moment that induces a transient random walk on $H$, the permutation coordinate of the random walk almost surely stabilizes pointwise. Our main result states that for $H=\mathbb{Z}$, the above convergence completely describes the Poisson boundary of the random walk $(\mathrm{FSym}(\mathbb{Z})\rtimes \mathbb{Z},μ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08878 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Poisson boundary of lampshuffler groups Silva, Eduardo Group Theory Probability We study random walks on the lampshuffler group $\mathrm{FSym}(H)\rtimes H$, where $H$ is a finitely generated group and $\mathrm{FSym}(H)$ is the group of finitary permutations of $H$. We show that for any step distribution $μ$ with a finite first moment that induces a transient random walk on $H$, the permutation coordinate of the random walk almost surely stabilizes pointwise. Our main result states that for $H=\mathbb{Z}$, the above convergence completely describes the Poisson boundary of the random walk $(\mathrm{FSym}(\mathbb{Z})\rtimes \mathbb{Z},μ)$. |
| title | The Poisson boundary of lampshuffler groups |
| topic | Group Theory Probability |
| url | https://arxiv.org/abs/2307.08878 |