From limit theorems to mixing limit theorems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916261719441408 |
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| author | Arana-Herrera, Francisco Forni, Giovanni |
| author_facet | Arana-Herrera, Francisco Forni, Giovanni |
| contents | Motivated by work of Dolgopyat and Nándori, we establish a general method for upgrading limit theorems for Birkhoff sums and cocycles over dynamical systems to mixing limit theorems under mild ergodicity and hyperbolicity assumptions. Building on previous work of Al-Saqban and Forni, we apply this method to obtain mixing limit theorems for particular subbundles of the Kontsevich-Zorich cocycle. In forthcoming work of Arana-Herrera and Honaryar these results are applied to study the arithmetic/homological complexity of long simple closed geodesics on negatively curved surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From limit theorems to mixing limit theorems Arana-Herrera, Francisco Forni, Giovanni Dynamical Systems Geometric Topology Probability Motivated by work of Dolgopyat and Nándori, we establish a general method for upgrading limit theorems for Birkhoff sums and cocycles over dynamical systems to mixing limit theorems under mild ergodicity and hyperbolicity assumptions. Building on previous work of Al-Saqban and Forni, we apply this method to obtain mixing limit theorems for particular subbundles of the Kontsevich-Zorich cocycle. In forthcoming work of Arana-Herrera and Honaryar these results are applied to study the arithmetic/homological complexity of long simple closed geodesics on negatively curved surfaces. |
| title | From limit theorems to mixing limit theorems |
| topic | Dynamical Systems Geometric Topology Probability |
| url | https://arxiv.org/abs/2405.16825 |