Random walks and Brownian motion: A method of computation for first-passage times and related quantities in confined geometries

Sylvain Condamin; Olivier Bénichou; Michel Moreau

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Random walks and Brownian motion: A method of computation for first-passage times and related quantities in confined geometries

Sylvain Condamin·Olivier Bénichou·Michel Moreau

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Abstract

In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a sphere. In both cases, we also discuss the case of two targets, including splitting probabilities, and conditional mean first-passage times. In addition, we study the higher-order moments and the full distribution of the first-passage time. These results significantly extend our earlier contribution [Phys. Rev. Lett. 95, 260601].

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Sylvain Condamin, Olivier Bénichou, Michel Moreau. 2007-01-08. Random walks and Brownian motion: A method of computation for first-passage times and related quantities in confined geometries. https://arxiv.org/abs/cond-mat/0610231

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