Encounter distribution of two random walkers on a finite one-dimensional interval

V. Tejedor , M. Schad , O. Benichou , R. Voituriez , R. Metzler

Bibtex , URL
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44, 39
Published 30 Sep. 2011
DOI: 10.1088/1751-8113/44/39/395005
ISSN: 1751-8113

Abstract

We analyse the first-passage properties of two random walkers confined to a finite one-dimensional domain. For the case of absorbing boundaries at the endpoints of the interval, we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries. For the case of reflecting boundaries, we obtain the mean first encounter time of the two particles. Our approach leads to closed-form expressions that are more easily tractable than a previously derived solution in terms of the Weierstrass' elliptic function.

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Stochastic dynamics of reactive and living systems