The Poisson boundary of Thompson's group $T$ is not the circle
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912305460019200 |
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| author | Vio, Martín Gilabert Kravaris, Cosmas Silva, Eduardo |
| author_facet | Vio, Martín Gilabert Kravaris, Cosmas Silva, Eduardo |
| contents | Let $μ$ be a nondegenerate probability measure with finite entropy on a countable group $G \leq \mathrm{Homeo}_+(S^1)$ of orientation-preserving homeomorphisms of the circle acting proximally, minimally and topologically nonfreely on $S^1$. We prove that the circle $S^1$ endowed with its unique $μ$-stationary probability measure is not the Poisson boundary of $(G,μ)$. When $G$ is Thompson's group $T$ and $μ$ is finitely supported, this answers a question posed by B. Deroin [Ergodic Theory Dynam. Systems, 2013] and A. Navas [Proceedings of the International Congress of Mathematicians, 2018]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01283 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Poisson boundary of Thompson's group $T$ is not the circle Vio, Martín Gilabert Kravaris, Cosmas Silva, Eduardo Dynamical Systems Group Theory Probability Let $μ$ be a nondegenerate probability measure with finite entropy on a countable group $G \leq \mathrm{Homeo}_+(S^1)$ of orientation-preserving homeomorphisms of the circle acting proximally, minimally and topologically nonfreely on $S^1$. We prove that the circle $S^1$ endowed with its unique $μ$-stationary probability measure is not the Poisson boundary of $(G,μ)$. When $G$ is Thompson's group $T$ and $μ$ is finitely supported, this answers a question posed by B. Deroin [Ergodic Theory Dynam. Systems, 2013] and A. Navas [Proceedings of the International Congress of Mathematicians, 2018]. |
| title | The Poisson boundary of Thompson's group $T$ is not the circle |
| topic | Dynamical Systems Group Theory Probability |
| url | https://arxiv.org/abs/2504.01283 |