On the empirical distribution of eigenvalues of a class of large dimensional random matrices

@article{Silverstein1995OnTE,
  title={On the empirical distribution of eigenvalues of a class of large dimensional random matrices},
  author={Jack W. Silverstein and Zhidong Bai},
  journal={Journal of Multivariate Analysis},
  year={1995},
  volume={54},
  pages={175-192}
}
A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marcenko and Pastur, is presented. Here, X(N - n), T(n - n), and A(N - N) are independent, with X containing i.i.d. entries having finite second moments, T is diagonal with real (diagonal) entries, A is Hermitian, and n/N --> c > 0 as N --> [infinity]. Under additional assumptions on the eigenvalues of A and T, almost sure convergence of the empirical… 
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