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Spectrum of random Toeplitz matrices with band structure


 
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1. Title Title of document Spectrum of random Toeplitz matrices with band structure
 
2. Creator Author's name, affiliation, country Vladislav Kargin; Stanford University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random matrices
 
3. Subject Subject classification 15A52
 
4. Description 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.
 
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6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2009-09-30
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1492
 
10. Identifier Digital Object Identifier 10.1214/ECP.v14-1492
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 14
 
12. Language English=en
 
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