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Non-white Wishart ensembles

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  • Péché, S.

Abstract

We consider non-white Wishart ensembles , where X is a pxN random matrix with i.i.d. complex standard Gaussian entries and [Sigma] is a covariance matrix, with fixed eigenvalues, close to the identity matrix. We prove that the largest eigenvalue of such random matrix ensembles exhibits a universal behavior in the large-N limit, provided [Sigma] is "close enough" to the identity matrix. If not, we identify the limiting distribution of the largest eigenvalues, focusing on the case where the largest eigenvalues almost surely exit the support of the limiting Marchenko-Pastur's distribution.

Suggested Citation

  • Péché, S., 2006. "Non-white Wishart ensembles," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 874-894, April.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:4:p:874-894
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    References listed on IDEAS

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    1. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    2. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
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