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

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

2006-10-09

arxiv.org/abs/cond-mat/0610231v2

Physics

Condensed Matter

Statistical Mechanics

49 pages, 22 figures. To be published in Phys.Rev.E

Scientific paper

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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