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Title: Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions
Authors: Daems, Evi
Kuijlaars, Arno # ×
Issue Date: 2007
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Series Title: Journal of approximation theory vol:146 issue:1 pages:91-114
Abstract: We present a generalization of multiple orthogonal polynomials of types I and II, which we call multiple orthogonal polynomials of mixed type. Some basic properties are formulated, and a Riemann-Hilbert problem for the multiple orthogonal polynomials of mixed type is given. We derive a Christoffel-Darboux formula for these polynomials using the solution of the Riemann-Hilbert problem. The main motivation for studying these polynomials comes from a model of non-intersecting one-dimensional Brownian motions with a given number of starting points and endpoints. The correlation kernel for the positions of the Brownian paths at any intermediate time coincides with the Christoffel-Darboux kernel for the multiple orthogonal polynomials of mixed type with respect to Gaussian weights.
ISSN: 0021-9045
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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