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


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.


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Vladislav Kargin. "Spectrum of random Toeplitz matrices with band structure." Electron. Commun. Probab. 14 412 - 423, 2009.


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

Primary: 15A52

Keywords: random matrices

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