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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| Accès en ligne: | https://arxiv.org/abs/2209.02246 |
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| _version_ | 1866909126168150016 |
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| author | Biskup, Marek Pan, Minghao |
| author_facet | Biskup, Marek Pan, Minghao |
| contents | We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the conductance law under space-time shifts and a moment assumption on the time to accumulate a unit conductance over a given edge, we prove that the walk scales, under a diffusive scaling of space and time, to a non-degenerate Brownian motion for a.e. realization of the environment. The conclusion particularly applies to random walks on one-dimensional dynamical percolation subject to fairly general stationary edge-flip dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02246 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An invariance principle for one-dimensional random walks in degenerate dynamical random environments Biskup, Marek Pan, Minghao Probability Mathematical Physics Analysis of PDEs 60K37, 82C41, 74Q10 We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the conductance law under space-time shifts and a moment assumption on the time to accumulate a unit conductance over a given edge, we prove that the walk scales, under a diffusive scaling of space and time, to a non-degenerate Brownian motion for a.e. realization of the environment. The conclusion particularly applies to random walks on one-dimensional dynamical percolation subject to fairly general stationary edge-flip dynamics. |
| title | An invariance principle for one-dimensional random walks in degenerate dynamical random environments |
| topic | Probability Mathematical Physics Analysis of PDEs 60K37, 82C41, 74Q10 |
| url | https://arxiv.org/abs/2209.02246 |