Open Access
Translator Disclaimer
January 1997 Circular law
Z. D. Bai
Ann. Probab. 25(1): 494-529 (January 1997). DOI: 10.1214/aop/1024404298

Abstract

It was conjectured in the early 1950’s that the empirical spectral distribution of an $n \times n$ matrix, of iid entries, normalized by a factor of $\frac{1}{\sqrt{n}}$, converges to the uniform distribution over the unit disc on the complex plane, which is called the circular law. Only a special case of the conjecture, where the entries of the matrix are standard complex Gaussian, is known. In this paper, this conjecture is proved under the existence of the sixth moment and some smoothness conditions. Some extensions and discussions are also presented.

Citation

Download Citation

Z. D. Bai. "Circular law." Ann. Probab. 25 (1) 494 - 529, January 1997. https://doi.org/10.1214/aop/1024404298

Information

Published: January 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0871.62018
MathSciNet: MR1428519
Digital Object Identifier: 10.1214/aop/1024404298

Subjects:
Primary: 60F15
Secondary: 62H99

Rights: Copyright © 1997 Institute of Mathematical Statistics

JOURNAL ARTICLE
36 PAGES


SHARE
Vol.25 • No. 1 • January 1997
Back to Top