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[Lecture] Applied Mathematics Seminar——Anomalous transport, fractional master equation and random walk of heterogeneous populations
Mar. 19, 2024
Speaker: Prof. Sergei Fedotov (University of Manchester)

Time: 10:15-11:15 a.m., March 19, 2024, GMT+8

Venue: Siyuan Hall, Zhihua Building, PKU


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.

Source: School of Mathematical Sciences, PKU