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On the joint residence time of N independent two-dimensional Brownian motions

O. Benichou·M. Coppey·J. Klafter·M. Moreau·G. Oshanin
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Abstract

We study the behavior of several joint residence times of N independent Brownian particles in a disc of radius $R$ in two dimensions. We consider: (i) the time T_N(t) spent by all N particles simultaneously in the disc within the time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N particles spend together in the disc within the time interval [0,t]; and (iii) the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend together in the disc within the time interval [0,t]. We obtain very simple exact expressions for the expectations of these three residence times in the limit t\to\infty.

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O. Benichou, M. Coppey, J. Klafter, M. Moreau, G. Oshanin. 2003-09-29. On the joint residence time of N independent two-dimensional Brownian motions. https://doi.org/10.1088/0305-4470%2F36%2F26%2F301

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