Abstract
This article proves that the spectral distribution of the random matrix $(1/2\sqrt{np}) (X_pX'_p)$, where $X_p = \lbrack X_{ij}\rbrack_{p\times n}$ and $\lbrack X_{ij}: i, j = 1,2,\ldots\rbrack$ has iid entries with $EX^4_{11} < \infty, \operatorname{Var}(X_{11}) = 1$, tends to the semicircle law as $p \rightarrow \infty, p/n \rightarrow 0$, a.s.
Citation
Z. D. Bai. Y. Q. Yin. "Convergence to the Semicircle Law." Ann. Probab. 16 (2) 863 - 875, April, 1988. https://doi.org/10.1214/aop/1176991792
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