On the joint residence time of N independent two-dimensional Brownian motions
Abstract
We study the behaviour of several joint residence times of N independent Brownian particles in a disc of radius R in two dimensions. We consider: (i) the time TN(t) spent by all N particles simultaneously in the disc within the time interval [0, t], (ii) the time T(m)N(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(m)N(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 rightarrow infty.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- July 2003
- DOI:
- 10.1088/0305-4470/36/26/301
- arXiv:
- arXiv:cond-mat/0309657
- Bibcode:
- 2003JPhA...36.7225B
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 8 pages