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Spectrum of random Toeplitz matrices with band structure

   
@article{ECP1492,
	author = {Vladislav Kargin},
	title = {Spectrum of random Toeplitz matrices with band structure},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {14},
	year = {2009},
	keywords = {random matrices},
	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.},
	pages = {no. 40, 412-423},
	issn = {1083-589X},
	doi = {10.1214/ECP.v14-1492},    
        url = {http://ecp.ejpecp.org/article/view/1492}}