Abstract:

Using the method of Stieltjes transform, we gave the explicit expressions of the limiting spectral density functions of the general high dimensional sample covariance matrices, which included: the sample covariance matrix whose elements were independent with zero mean and constant variance; the sum of a sample covariance matrix and a unit matrix; the sample covariance matrix which satisfied that the variance of the elements were different but only had two values; the sum of two different sample covariance matrices.

Key words: random matrix, limiting spectral density (LSD) function, sample covariance matrix