Electronic Communications in Probability

Spectrum of random Toeplitz matrices with band structure

Vladislav Kargin

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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.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 40, 412-423.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234749

Digital Object Identifier
doi:10.1214/ECP.v14-1492

Mathematical Reviews number (MathSciNet)
MR2551851

Zentralblatt MATH identifier
1188.15036

Subjects
Primary: 15A52

Keywords
random matrices

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Kargin, Vladislav. Spectrum of random Toeplitz matrices with band structure. Electron. Commun. Probab. 14 (2009), paper no. 40, 412--423. doi:10.1214/ECP.v14-1492. https://projecteuclid.org/euclid.ecp/1465234749


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