Exact dynamics of diffusive search processes in disordered systems: application to sparse networks

by Prof. Luca Giuggioli (University of Bristol)

Thursday 29 Jan 2026, 11:30 → 12:30 Asia/Kolkata

A 304 and on zoom

Quantifying how spatial disorder affects the movement of a diffusing particle or an agent is fundamental to a myriad of applications across disciplines. When diffusion occurs on a network, that is on a highly disordered environment, predicting the movement dynamics of an agent has relied so far on estimates provided by stochastic simulations, rather than rigorous mathematical tools. To close this knowledge gap we have devised a general methodology to represent analytically the movement and search dynamics of a diffusing random walk on sparse graphs. We show its utility by uncovering the existence of a bi-modality regime in the time-dependence of the first-passage probability to hit a target node in a small-world network. By identifying the network features that give rise to the bi-modal regime, we 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.

Reference: https://arxiv.org/pdf/2508.10140