On equivalence of quenched and annealed statistical properties for conservative IID random dynamical systems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914023151239168 |
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| author | DeWitt, Jonathan Dolgopyat, Dmitry |
| author_facet | DeWitt, Jonathan Dolgopyat, Dmitry |
| contents | In this paper, we prove several theorems relating annealed exponential mixing of the two-point motion with quenched properties of the one-point motion for conservative IID random dynamical systems. In particular, we show that annealed exponential mixing of the two-point motion implies quenched exponential mixing of the one-point motion. We also show that if the two-point motion satisfies annealed exponential mixing and the annealed central limit theorem with polynomial rate of convergence, then the one-point motion satisfies a quenched CLT. These results hold for all Hölder and Sobolev spaces of positive index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04740 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On equivalence of quenched and annealed statistical properties for conservative IID random dynamical systems DeWitt, Jonathan Dolgopyat, Dmitry Dynamical Systems Probability In this paper, we prove several theorems relating annealed exponential mixing of the two-point motion with quenched properties of the one-point motion for conservative IID random dynamical systems. In particular, we show that annealed exponential mixing of the two-point motion implies quenched exponential mixing of the one-point motion. We also show that if the two-point motion satisfies annealed exponential mixing and the annealed central limit theorem with polynomial rate of convergence, then the one-point motion satisfies a quenched CLT. These results hold for all Hölder and Sobolev spaces of positive index. |
| title | On equivalence of quenched and annealed statistical properties for conservative IID random dynamical systems |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2509.04740 |