Semicircle Law for a Class of Random Matrices with Dependent Entries

In this paper we study ensembles of random symmetric matrices ₙ = Xᵢⱼi,j = 1ⁿ with dependent entries such that Xᵢⱼ = 0, Xᵢⱼ² = σᵢⱼ², where σᵢⱼ may be different numbers. Assuming that the average of the normalized sums of variances in each row converges to one and Lindeberg condition holds we prove that the empirical spectral distribution of eigenvalues converges to Wigner's semicircle law.