ANALYSIS OF THE BEHAVIOR OF LIMITING SPECTRAL DENSITY FUNCTION OF LARGE DIMENSIONAL RANDOM MATRICES

Results on the analytic behavior of the limiting spectral distribution of large dimensional random matrices, studied in Marcenko and Pastur [2], are derived. Using the Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic whenever it is positive [3]. In the present paper, it is derived that the behavior of it resembles the behavior of a square root function near the boundary of its support.