SKLGP大讲堂：Anomalous transport, fractional master equation and random walk of heterogeneous populations

报告题目：Anomalous transport, fractional master equation and random walk of heterogeneous populations

报告人：Sergei Fedotov

报告人所在单位：The University of Manchester

报告时间：2024年03月26日16:00 — 17:30（周二）

报告地点：九教C座207

报告简介：

We present a random walk model that incorporates random transition probabilities among a heterogeneous population of random walkers, resulting in an effectively self-reinforcing random walk. The heterogeneity of the population leads to conditional transition probabilities that increase with the number of steps taken previously (self-reinforcement). We establish the connection between random walks with a heterogeneous ensemble and those with strong memory where the transition probability depends on the entire history of steps. We employ subordination, utilizing the fractional Poisson process to count the number of steps at a given time and the discrete random walk with self-reinforcement to determine the ensemble-averaged solution of the fractional master equation. We also find the exact solution for the variance which exhibits superdiffusion even as the fractional exponent tends to 1. We discuss the applications of this random walk model for intracellular transport and stochastic endocytosis. Given that a heterogeneous population of random walkers emulates strong memory, this opens another avenue for modeling biological processes that display strong memory properties and yet are heterogeneous ensembles of inanimate objects, such as organelles and macromolecules.

主办单位：成都理工大学数理学院

                 地质灾害防治与地质环境保护国家重点实验室

                 国际交流与合作处

                 数学地质四川省重点实验室

2024年3月22日