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Minima of Independent Bessel Processes and of Distances Between Brownian Particles
Author(s) -
Penrose Mathew D.
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-43.2.355
Subject(s) - brownian motion , maxima and minima , bessel function , interval (graph theory) , convergence (economics) , unit interval , space (punctuation) , statistical physics , mathematics , mathematical analysis , physics , combinatorics , computer science , statistics , economics , economic growth , operating system
Consider a large, finite collection of particles performing Brownian motion independently in space. We examine the process obtained by taking the minimum, at each time, of the distances of the particles, either (a) from the origin, or (b) from each other. In both cases, when time and space are suitably renormalized, we obtain a narrow convergence result. We also consider the number of pairs of particles which approach each other closely, over a unit time interval.