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2007 Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices
Arup Bose, Arnab Sen
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Electron. Commun. Probab. 12: 21-27 (2007). DOI: 10.1214/ECP.v12-1243

Abstract

Suppose $s_n$ is the spectral norm of either the Toeplitz or the Hankel matrix whose entries come from an i.i.d. sequence of random variables with positive mean $\mu$ and finite fourth moment. We show that $n^{-1/2}(s_n-n\mu)$ converges to the normal distribution in either case. This behaviour is in contrast to the known result for the Wigner matrices where $s_n-n\mu$ is itself asymptotically normal.

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Arup Bose. Arnab Sen. "Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices." Electron. Commun. Probab. 12 21 - 27, 2007. https://doi.org/10.1214/ECP.v12-1243

Information

Accepted: 13 February 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1130.60042
MathSciNet: MR2284045
Digital Object Identifier: 10.1214/ECP.v12-1243

Subjects:
Primary: 60F99
Secondary: 60F05, 60F15

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