Strong approximation of eigenvalues of large dimensional Wishart matrices by roots of generalized Laguerre polynomials

Authors:
Holger Dette
Affiliations:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
Venue:
Journal of Approximation Theory
Year:
2002

Citing 3
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Abstract

The purpose of this note is to establish a link between recent results on asymptotics for classical orthogonal polynomials and random matrix theory. Roughly speaking it is demonstrated that the ith eigenvalue of a Wishart matrix W(In, s) is close to the ith zero of an appropriately scaled Laguerre polynomial, when limn,s→∞ n/s = y ∈ [0, ∞). As a by-product we obtain an elemantary proof of the Marcenko-Pastur and the semicircle law without relying on combinatorical arguments.