Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices
نویسنده
چکیده
Let X be n×N containing i.i.d. complex entries with E|X11 − EX11| = 1, and T an n× n random Hermitian non-negative definite, independent of X. Assume, almost surely, as n →∞, the empirical distribution function (e.d.f.) of the eigenvalues of T converges in distribution, and the ratio n/N tends to a positive number. Then it is shown that, almost surely, the e.d.f. of the eigenvalues of (1/N)XX∗T converges in distribution. The limit is nonrandom and is characterized in terms of its Stieltjes transform, which satisfies a certain equation.
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