Events

Date: 1 October 2025   Time: 14:00 - 15:00

Location: Hybrid: School of Mathematical Sciences, MB503 or via the Teams link below

Abstract: Understanding how spatial disorder affects the random search of a diffusing particle or agent is fundamental to a myriad of applications across disciplines. To quantify how spatial heterogeneities may affect the dynamics of first-passage processes, I consider diffusion occurring on a network, that is on a highly disordered environment. In most instances predicting the movement dynamics of an agent on networks has relied so far on estimates provided by stochastic simulations, rather than rigorous mathematical tools. To close this knowledge gap I have devised a general methodology to represent analytically the movement and search dynamics of a diffusing random walk on a graph, which is particularly convenient for sparse graphs. By considering small-world networks, I have uncovered the existence of a bi-modality regime in the time-dependence of the first-passage probability to hit a target node. By identifying the network features that give rise to the bi-modal regime, I challenge long-held beliefs on how the statistics of the so-called direct, intermediate, and indirect trajectories influence the shape of the resulting first-passage and first-absorption probabilities and the interpretation of their mean values.

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