No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices

@article{Bai1998NoEO,
  title={No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices},
  author={Zhidong Bai and Jack W. Silverstein},
  journal={Annals of Probability},
  year={1998},
  volume={26},
  pages={316-345}
}
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… 

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