arXiv subjects

Yuanze Hong

Publications and source records attributed to Yuanze Hong.

2 recordsLinked to original sources

arXiv2025

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

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.

cond-mat.stat-mech↗

arXiv2024

Simulation of the continuous-time random walk using subordination schemes

The continuous time random walk model has been widely applied in various fields, including physics, biology, chemistry, finance, social phenomena, etc. In this work, we present an algorithm that utilizes a subordinate formula to generate data of the continuous time random walk in the long time limit. The algorithm has been validated using commonly employed observables, such as typical fluctuations of the positional distribution, rare fluctuations, the mean and the variance of the position, and breakthrough curves with time-dependent bias, demonstrating a perfect match.

cond-mat.stat-mech↗