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Title: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits
Authors: Kuijlaars, Arno # ×
Zhang, Lun #
Issue Date: Dec-2014
Publisher: Springer-Verlag Heidelberg
Series Title: Communications in Mathematical Physics vol:332 issue:2 pages:759-781
Abstract: Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that can be expressed in terms of Meijer G-functions. We show that this point process
can be interpreted as a multiple orthogonal polynomial ensemble. We give integral representations for the relevant multiple orthogonal polynomials and a new double contour
integral for the correlation kernel, which allows us to find its scaling limits at the origin (hard edge). The limiting kernels generalize the classical Bessel kernels. For M = 2 they coincide with the scaling limits found by Bertola, Gekhtman, and Szmigielski in the Cauchy–Laguerre two-matrix model, which indicates that these kernels represent a new universality class in random matrix theory.
ISSN: 0010-3616
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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