Title: Asymptotics of non-intersecting Brownian motions and a 4x4 Riemann-Hilbert problem
Authors: Daems, Evi
Kuijlaars, Arno ×
Veys, Willem #
Issue Date: Aug-2008
Publisher: Academic Press
Series Title: Journal of approximation theory vol:153 issue:2 pages:225-256
Abstract: We consider n one-dimensional Brownian motions, such that n/2 Brownian motions start at time t=0 in the starting point a and end at time t=1 in the endpoint b and the other n/2 Brownian motions start at time t=0 at the point -a and end at time t=1 in the point -b, conditioned that the n Brownian paths do not intersect in the whole time interval (0,1). The correlation functions of the positions of the non-intersecting Brownian motions have a determinantal form with a kernel that is expressed in terms of multiple Hermite polynomials of mixed type. We analyze this kernel in the large n limit of the case ab < 1/2. We find that the limiting mean density of the positions of the Brownian motions is supported on one or two intervals and that the correlation kernel has the usual scaling limits from random matrix theory, namely the sine kernel in the bulk and the Airy kernel near the edges.
ISSN: 0021-9045
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
Analysis Section
× corresponding author
# (joint) last author

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