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This article proves that the spectral distribution of the random matrix (1/2np) (XₚX'ₚ), where Xₚ = X₈₉ ₍ and X₈₉: i, j = 1, 2, has iid entries with EX⁴₁₁ <, Var (X₁₁) = 1, tends to the semicircle law as p, p/n 0, a. s.
Bai et al. (Fri,) studied this question.