# Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices

@article{Silverstein1995StrongCO, title={Strong convergence of the empirical distribution of eigenvalues of large dimensional random matrices}, author={Jack W. Silverstein}, journal={Journal of Multivariate Analysis}, year={1995}, volume={55}, pages={331-339} }

Let X be n - N containing i.i.d. complex entries with E X11 - EX112 = 1, and T an n - n random Hermitian nonnegative definite, independent of X. Assume, almost surely, as n --> [infinity], 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…

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