Open Access
Translator Disclaimer
July 2010 The circular law for random matrices
Friedrich Götze, Alexander Tikhomirov
Ann. Probab. 38(4): 1444-1491 (July 2010). DOI: 10.1214/09-AOP522

Abstract

We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries. We assume that the entries have a finite moment of order larger than two and consider the case of sparse matrices.

The results are based on previous work of Bai, Rudelson and the authors extending those results to a larger class of sparse matrices.

Citation

Download Citation

Friedrich Götze. Alexander Tikhomirov. "The circular law for random matrices." Ann. Probab. 38 (4) 1444 - 1491, July 2010. https://doi.org/10.1214/09-AOP522

Information

Published: July 2010
First available in Project Euclid: 8 July 2010

zbMATH: 1203.60010
MathSciNet: MR2663633
Digital Object Identifier: 10.1214/09-AOP522

Subjects:
Primary: 60K35 , 60K35
Secondary: 60K35

Keywords: circular law , random matrices

Rights: Copyright © 2010 Institute of Mathematical Statistics

JOURNAL ARTICLE
48 PAGES


SHARE
Vol.38 • No. 4 • July 2010
Back to Top