Semicircle Law for a Class of Random Matrices with Dependent Entries
Götze, F. · Naumov, A. · Tikhomirov, A.
Original · EN
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.
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