The probability of an encounter of two Brownian particles before escape

Details The probability of an encounter of two Brownian particles before escape The probability of an encounter of two Brownian particles before escape

2009-06-19

arxiv.org/abs/0906.3631v1

Physics

Mathematical Physics

To appear J. Phys A

Scientific paper

We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of the two particles using the Weierstrass elliptic function. We also find the law of the meeting location. Brownian simulations show the accuracy of our analysis. Finally, we discuss some applications to the probability that a double strand DNA break repairs in confined environments.

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