The Unique stationary boundary property
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916234922033152 |
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| author | Glasner, Eli |
| author_facet | Glasner, Eli |
| contents | Let $G$ be a locally compact group and $μ$ an admissible probability measure on $G$. Let $(B,ν)$ be the universal topological Poisson $μ$-boundary of $(G,μ)$ and $Π_s(G)$ the universal minimal strongly proximal $G$-flow. This note is inspired by a recent result of Hartman and Kalantar. We show that for a locally compact second countable group $G$ the following conditions are equivalent: (i) the measure $ν$ is the unique $μ$-stationary measure on $B$, (ii) $(B,G) \cong (Π_s(G),G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Unique stationary boundary property Glasner, Eli Dynamical Systems Group Theory Probability 22D40, 37A50, 37B05 Let $G$ be a locally compact group and $μ$ an admissible probability measure on $G$. Let $(B,ν)$ be the universal topological Poisson $μ$-boundary of $(G,μ)$ and $Π_s(G)$ the universal minimal strongly proximal $G$-flow. This note is inspired by a recent result of Hartman and Kalantar. We show that for a locally compact second countable group $G$ the following conditions are equivalent: (i) the measure $ν$ is the unique $μ$-stationary measure on $B$, (ii) $(B,G) \cong (Π_s(G),G)$. |
| title | The Unique stationary boundary property |
| topic | Dynamical Systems Group Theory Probability 22D40, 37A50, 37B05 |
| url | https://arxiv.org/abs/2404.18140 |