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

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

2003-09-29

arxiv.org/abs/cond-mat/0309657v1

J. Phys. A 36, 7225 (2003)

Physics

Condensed Matter

Statistical Mechanics

8 pages

Scientific paper

10.1088/0305-4470/36/26/301

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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