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Random block matrices generalizing the classical Jacobi and Laguerre ensembles

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  • Guhlich, Matthias
  • Nagel, Jan
  • Dette, Holger

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.

Suggested Citation

  • Guhlich, Matthias & Nagel, Jan & Dette, Holger, 2010. "Random block matrices generalizing the classical Jacobi and Laguerre ensembles," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1884-1897, September.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1884-1897
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    References listed on IDEAS

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    1. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    2. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
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