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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2312.01390 |
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| _version_ | 1866917697900511232 |
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| author | Jin, Xiong |
| author_facet | Jin, Xiong |
| contents | We prove a Chung-Fuchs type theorem for skew product dynamical systems such that for a measurable function on such a system, if its Birkhoff average converges to zero almost surely, and on typical fibres its Birkhoff sums have a non-trivial independent structure, then its associated generalised random walk oscillates, that is the supremum of the random walk equals to $+\infty$ and the infimum equals to $-\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01390 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Chung-Fuchs type theorem for skew product dynamical systems Jin, Xiong Dynamical Systems Probability We prove a Chung-Fuchs type theorem for skew product dynamical systems such that for a measurable function on such a system, if its Birkhoff average converges to zero almost surely, and on typical fibres its Birkhoff sums have a non-trivial independent structure, then its associated generalised random walk oscillates, that is the supremum of the random walk equals to $+\infty$ and the infimum equals to $-\infty$. |
| title | A Chung-Fuchs type theorem for skew product dynamical systems |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2312.01390 |