Ergodicity of (co)expanding on average random dynamical systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913149646536704 |
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| author | DeWitt, Jonathan Dolgopyat, Dmitry Zhang, Zhiyuan |
| author_facet | DeWitt, Jonathan Dolgopyat, Dmitry Zhang, Zhiyuan |
| contents | We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\in \mathrm{SO}(d+1)$, $d\ge 2$, generate a dense subgroup, then the random dynamics of $R_1$ and $R_2$ on $S^d$ is stably ergodic. Previously this was only known to hold in even dimensions. As a consequence, we deduce spectral gap and statistical limit theorems for such systems. In particular, our results apply in the presence of zero Lyapunov exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ergodicity of (co)expanding on average random dynamical systems DeWitt, Jonathan Dolgopyat, Dmitry Zhang, Zhiyuan Dynamical Systems We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\in \mathrm{SO}(d+1)$, $d\ge 2$, generate a dense subgroup, then the random dynamics of $R_1$ and $R_2$ on $S^d$ is stably ergodic. Previously this was only known to hold in even dimensions. As a consequence, we deduce spectral gap and statistical limit theorems for such systems. In particular, our results apply in the presence of zero Lyapunov exponents. |
| title | Ergodicity of (co)expanding on average random dynamical systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.21199 |