Convergence Rates Of Spectral Distribution Of Wigner Type Matrices

Let Wn be n × n Hermitian whose entries on and above the diagonal are independent complex random variables, with mean zero and variance one. Let Tn be a n × n non-random positive definitive matrix. Assume that as n ? ?, the empirical distribution of Tn converges weakly to a probability distribution. Let An = n-1/2Tn1/2WnTn1/2. Then with the aid of the Stieltjes transforms, we show that if supn supi,j E|xij16|<?,as n??, we obtain that the rate of the expected empirical spectral distribution of An converging to its limit spectral distribution is O(n-1/5).