Random block matrices generalizing the classical Jacobi and Laguerre ensembles |
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Authors: | Matthias Guhlich Holger Dette |
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Institution: | Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany |
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Abstract: | In this paper we consider random block matrices which generalize the classical Laguerre ensemble and the Jacobi ensemble. We show that the random eigenvalues of the matrices can be uniformly approximated by the zeros of matrix orthogonal polynomials and obtain a rate for the maximum difference between the eigenvalues and the zeros. This relation between the random block matrices and matrix orthogonal polynomials allows a derivation of the asymptotic spectral distribution of the matrices. |
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Keywords: | 60B20 33C45 |
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