ANALYSIS OF THE LIMITING SPECTRAL DISTRIBUTION OF LARGE DIMENSIONAL RANDOM MATRICES

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 root\x-x(o)\ for most cases of x(o) in the boundary of its support. A complete analysis of a way to determine its support, originally outlined in Marenko and Pastur [2], is also presented. (C) 1995 Academic Press, Inc.