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April, 1988 Convergence to the Semicircle Law
Z. D. Bai, Y. Q. Yin
Ann. Probab. 16(2): 863-875 (April, 1988). DOI: 10.1214/aop/1176991792


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.


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Z. D. Bai. Y. Q. Yin. "Convergence to the Semicircle Law." Ann. Probab. 16 (2) 863 - 875, April, 1988.


Published: April, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0648.60030
MathSciNet: MR929083
Digital Object Identifier: 10.1214/aop/1176991792

Primary: 60F99
Secondary: 62E20

Keywords: Random matrix , semicircle law , Spectral distribution

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 2 • April, 1988
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