Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices

J. W. Silverstein and S. I. Choi

Journal of Multivariate Analysis, 1995, vol. 54, issue 2, 295-309

Abstract: Results on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied in Marcenko and Pastur [2] and Yin [8], are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and resembles [formula] for most cases of x0 in the boundary of its support. A complete analysis of a way to determine its support, originally outlined in Marcenko and Pastur [2], is also presented.

Date: 1995
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