Random walks and Brownian motion: a method of computation for first-passage times and related quantities in confined geometries.
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 [Condamin, Phys. Rev. Lett. 95, 260601 (2005)].
Condamin
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Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), Case Courrier 121, Université Paris 6, 4 Place Jussieu, 75255 Paris Cedex, France.
Bénichou
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Moreau
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