2003/06/17 by O B nichou, O. Benichou, M. Coppey +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Point processes and geometric inequalities #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/36/26/301
published as J. Phys. A 36, 7225 (2003) · 8 pages
openalex publication_date 2003/06/17 · arxiv created 2003/09/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 T N ( 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 ( 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 → ∞ .