Convergence to the Semicircle Law

This article proves that the spectral distribution of the random matrix (1/2√np) (XₚX'ₚ), where Xₚ = Xᵢⱼp× n and Xᵢⱼ: i, j = 1,2,… has iid entries with EX⁴₁₁ < ∞, Var(X₁₁) = 1, tends to the semicircle law as p → ∞, p/n → 0, a.s.