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

  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},
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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  • K. Fan
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1951