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Jacobi polynomial moments and products of random matrices


Authors: Wolfgang Gawronski, Thorsten Neuschel and Dries Stivigny
Journal: Proc. Amer. Math. Soc. 144 (2016), 5251-5263
MSC (2010): Primary 30E05; Secondary 15B52, 30F10, 46L54
DOI: https://doi.org/10.1090/proc/13153
Published electronically: June 10, 2016
MathSciNet review: 3556269
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Abstract: Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class of measures and characterize them by their moments essentially given by specific Jacobi polynomials with varying parameters. Solving this moment problem requires a study of the Riemann surfaces associated to a class of algebraic equations. The connection to random matrix theory is then established using methods from free probability.


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Additional Information

Wolfgang Gawronski
Affiliation: Department of Mathematics, University of Trier, 54286 Trier, Germany
Email: gawron@uni-trier.de

Thorsten Neuschel
Affiliation: Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-La-Neuve, Belgium
Email: thorsten.neuschel@uclouvain.be

Dries Stivigny
Affiliation: Department of Mathematics, KU Leuven, Celestijnenlaan 200B box 2400, BE-3001 Leuven, Belgium
Email: dries.stivigny@wis.kuleuven.be

DOI: https://doi.org/10.1090/proc/13153
Keywords: Moment problem, Jacobi polynomials, Raney distributions, random matrices, distribution of eigenvalues, free probability theory, free multiplicative convolution
Received by editor(s): August 26, 2014
Received by editor(s) in revised form: February 15, 2016
Published electronically: June 10, 2016
Communicated by: Mourad Ismail
Article copyright: © Copyright 2016 American Mathematical Society

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