Title: A note on the limiting mean distribution of singular values for products of two Wishart random matrices
Authors: Zhang, Lun # ×
Issue Date: Aug-2013
Publisher: American Institute of Physics
Series Title: Journal of Mathematical Physics vol:54 pages:1-8
Article number: 083303
Abstract: The product of M complex random Gaussian matrices of size
N has recently been studied by Akemann, Kieburg, and Wei. They showed that, for fixed M and N, the
joint probability distribution for the squared singular values of the product matrix forms a determinantal point process with a correlation kernel determined by certain
biorthogonal polynomials that can be explicitly constructed. We find that, in the case M = 2, the relevant biorthogonal polynomials are actually special cases of
multiple orthogonal polynomials associated with Macdonald functions (modified Bessel functions of the second kind) which was first introduced by Van Assche and
Yakubovich. With known results on asymptotic zero distribution of these polynomials
and general theory on multiple orthogonal polynomial ensembles, it is then easy to
obtain an explicit expression for the distribution of squared singular values for the
product of two complex random Gaussian matrices in the limit of large matrix dimensions.
ISSN: 0022-2488
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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