Convergence to the Semicircle Law

Bai, Z. D. ; Yin, Y. Q.

Ann. Probab., Tome 16 (1988) no. 4, p. 863-875 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1988-04-14
Classification:  Random matrix,  spectral distribution,  semicircle law,  60F99,  62E20