@article{bai_silverstein_1998, title={No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices}, volume={26}, DOI={10.1214/aop/1022855421}, abstractNote={Let B n = (1/N)T n 1/2 X n X n *Tn 1/2 , where X n is n x N with i.i.d. complex standardized entries having finite fourth moment and T n 1/2 is a Hermitian square root of the nonnegative definite Hermitian matrix T n . It is known that, as n → ∞, if n/N converges to a positive number and the empirical distribution of the eigenvalues of T n converges to a proper probability distribution, then the empirical distribution of the eigenvalues of B n converges a.s. to a nonrandom limit. In this paper we prove that, under certain conditions on the eigenvalues of T n , for any closed interval outside the support of the limit, with probability 1 there will be no eigenvalues in this interval for all n sufficiently large.}, number={1}, journal={Annals of Probability}, author={Bai, Z. D. and Silverstein, Jack W.}, year={1998}, pages={316–345} }