Local limit theorems for expanding maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929417808248832 |
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| author | Dolgopyat, Dmitry Hafouta, Yeor |
| author_facet | Dolgopyat, Dmitry Hafouta, Yeor |
| contents | We prove local central limit theorems for partial sums of the form \newline $\,S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where $f_j$ are uniformly Hölder functions and $T_j$ are expanding maps. Using a symbolic representation a similar result follows for maps $T_j$ in a small $C^1$ neighborhood of an Axiom A map and Hölder continuous functions $f_j$. All of our results are already new when all maps are the same $T_j=T$ but observables $(f_j)$ are different. The current paper compliments [43] where Berry--Esseen theorems are obtained. An important step in the proof is developing an appropriate reduction theory in the sequential case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local limit theorems for expanding maps Dolgopyat, Dmitry Hafouta, Yeor Dynamical Systems Probability We prove local central limit theorems for partial sums of the form \newline $\,S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where $f_j$ are uniformly Hölder functions and $T_j$ are expanding maps. Using a symbolic representation a similar result follows for maps $T_j$ in a small $C^1$ neighborhood of an Axiom A map and Hölder continuous functions $f_j$. All of our results are already new when all maps are the same $T_j=T$ but observables $(f_j)$ are different. The current paper compliments [43] where Berry--Esseen theorems are obtained. An important step in the proof is developing an appropriate reduction theory in the sequential case. |
| title | Local limit theorems for expanding maps |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2407.08690 |