Translator Disclaimer
2009 Spectrum of random Toeplitz matrices with band structure
Vladislav Kargin
Author Affiliations +
Electron. Commun. Probab. 14: 412-423 (2009). DOI: 10.1214/ECP.v14-1492

Abstract

This paper considers the eigenvalues of symmetric Toeplitz matrices with independent random entries and band structure. We assume that the entries of the matrices have zero mean and a uniformly bounded 4th moment, and we study the limit of the eigenvalue distribution when both the size of the matrix and the width of the band with non-zero entries grow to infinity. It is shown that if the bandwidth/size ratio converges to zero, then the limit of the eigenvalue distributions is Gaussian. If the ratio converges to a positive limit, then the distributions converge to a non-Gaussian distribution, which depends only on the limit ratio. A formula for the fourth moment of this distribution is derived.

Citation

Download Citation

Vladislav Kargin. "Spectrum of random Toeplitz matrices with band structure." Electron. Commun. Probab. 14 412 - 423, 2009. https://doi.org/10.1214/ECP.v14-1492

Information

Accepted: 30 September 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1188.15036
MathSciNet: MR2551851
Digital Object Identifier: 10.1214/ECP.v14-1492

Subjects:
Primary: 15A52

Keywords: random matrices

JOURNAL ARTICLE
12 PAGES


SHARE
Back to Top