Non-white Wishart ensembles

S. Péché

Journal of Multivariate Analysis, 2006, vol. 97, issue 4, 874-894

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.

Keywords: Random; matrix; Sample; covariance; matrices; Largest; eigenvalue; Wishart; matrix (search for similar items in EconPapers)
Date: 2006
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