Random block matrices generalizing the classical ensembles

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 roots of matrix orthogonal polynomials and obtain a rate for the maximum difference between the eigenvalues and the roots. This relation between the random block matrices and matrix orthogonal polynomials allows a derivation of the asymptotic spectral distribution of the matrices