The Annals of Probability

Convergence to the Semicircle Law

Z. D. Bai and Y. Q. Yin

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 863-875.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991792

Digital Object Identifier
doi:10.1214/aop/1176991792

Mathematical Reviews number (MathSciNet)
MR929083

Zentralblatt MATH identifier
0648.60030

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 62E20: Asymptotic distribution theory

Keywords
Random matrix spectral distribution semicircle law

Citation

Bai, Z. D.; Yin, Y. Q. Convergence to the Semicircle Law. Ann. Probab. 16 (1988), no. 2, 863--875. doi:10.1214/aop/1176991792. https://projecteuclid.org/euclid.aop/1176991792


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