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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2411.09989 |
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| _version_ | 1866916616447459328 |
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| author | Hong, Yuanze zhou, Tian Wang, Wanli |
| author_facet | Hong, Yuanze zhou, Tian Wang, Wanli |
| contents | We explore the fractional advection-diffusion equation and rare events associated with the ACTRW model. When waiting times have a finite mean but infinite variance, and the displacements follow a narrow distribution, the fractional operator is defined in terms of space rather than time. The far tail of the positional distribution is governed by rare events, which exhibit a different scaling compared to typical fluctuations. Additionally, we establish a strong relationship between the number of renewals and the positional distribution in the context of large deviations. Throughout the manuscript, the theoretical results are validated through simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusion equation and rare fluctuations of the biased aging continuous-time random walk model Hong, Yuanze zhou, Tian Wang, Wanli Statistical Mechanics We explore the fractional advection-diffusion equation and rare events associated with the ACTRW model. When waiting times have a finite mean but infinite variance, and the displacements follow a narrow distribution, the fractional operator is defined in terms of space rather than time. The far tail of the positional distribution is governed by rare events, which exhibit a different scaling compared to typical fluctuations. Additionally, we establish a strong relationship between the number of renewals and the positional distribution in the context of large deviations. Throughout the manuscript, the theoretical results are validated through simulations. |
| title | Diffusion equation and rare fluctuations of the biased aging continuous-time random walk model |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2411.09989 |