THE INVERSION FORMULA OF THE STIELTJES TRANSFORM OF SPECTRAL DISTRIBUTION

Abstract

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let Bn = 1 m TmYm where Ym = [Yij ]m×n is with independent, identically distributed entries and Tm is an m × m symmetric nonnegative definite random matrix independent of the Yij 's. In the present paper, using the inversion formula of the Stieltjes transform, we will find the density function of the limiting distribution of Bn away from zero.

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