Diffusion equation and rare fluctuations of the biased aging continuous-time random walk model

Yuanze Hong; Tian zhou; Wanli Wang

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arXiv · 2411.09989

Diffusion equation and rare fluctuations of the biased aging continuous-time random walk model

Yuanze Hong·Tian zhou·Wanli Wang

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Abstract

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.

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Yuanze Hong, Tian zhou, Wanli Wang. 2024-11-15. Diffusion equation and rare fluctuations of the biased aging continuous-time random walk model. https://arxiv.org/abs/2411.09989

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