Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912253725376512 |
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| author | Allasia, Julien |
| author_facet | Allasia, Julien |
| contents | In this paper, we study random walks evolving on Z in a dynamic random environment that we assume to have time correlations that decrease polynomially fast. We show a law of large numbers by generalizing methods already used for the nearest-neighbor framework to the finite-range one. This requires some new ideas to get around the absence of a monotonicity property that was crucial in the proof for the nearest-neighbour case. Our proof works both in discrete and continuous time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03143 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing Allasia, Julien Probability In this paper, we study random walks evolving on Z in a dynamic random environment that we assume to have time correlations that decrease polynomially fast. We show a law of large numbers by generalizing methods already used for the nearest-neighbor framework to the finite-range one. This requires some new ideas to get around the absence of a monotonicity property that was crucial in the proof for the nearest-neighbour case. Our proof works both in discrete and continuous time. |
| title | Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing |
| topic | Probability |
| url | https://arxiv.org/abs/2304.03143 |