First-passage times for random walks in bounded domains
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Updated: Aug 11, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
S Condamin1, O Bénichou, M Moreau
1Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), case courrier 121, Université Paris 6, France.
Abstract:
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical simulations. Their range of validity is discussed. We also consider the case of a starting site and two targets. In addition, we present the extension to continuous Brownian motion. These results are of great relevance to any system involving diffusion in confined media.
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