## The Annals of Probability

### Convergence to the Semicircle Law

#### 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

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