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On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices

  • Silverstein, J. W.
  • Bai, Z. D.
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    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 distribution function of the eigenvalues of A + XTX* is proven with the aid of Stieltjes transforms, taking a more direct approach than previous methods.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 54 (1995)
    Issue (Month): 2 (August)
    Pages: 175-192

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    Handle: RePEc:eee:jmvana:v:54:y:1995:i:2:p:175-192
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