Non-white Wishart ensembles |
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Authors: | S Péché |
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Institution: | Institut Fourier, Université Joseph Fourier, BP 74, 38402 St Martin D’heres Cedex, France |
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Abstract: | We consider non-white Wishart ensembles , where X is a p×N random matrix with i.i.d. complex standard Gaussian entries and Σ 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 Σ 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. |
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Keywords: | 15A52 62E20 60F05 |
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