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November 2013 The top eigenvalue of the random Toeplitz matrix and the sine kernel
Arnab Sen, Bálint Virág
Ann. Probab. 41(6): 4050-4079 (November 2013). DOI: 10.1214/13-AOP863

Abstract

We show that the top eigenvalue of an $n\times n$ random symmetric Toeplitz matrix, scaled by $\sqrt{2n\log n}$, converges to the square of the $2\to4$ operator norm of the sine kernel.

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Arnab Sen. Bálint Virág. "The top eigenvalue of the random Toeplitz matrix and the sine kernel." Ann. Probab. 41 (6) 4050 - 4079, November 2013. https://doi.org/10.1214/13-AOP863

Information

Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1284.60020
MathSciNet: MR3161469
Digital Object Identifier: 10.1214/13-AOP863

Subjects:
Primary: 60F25
Secondary: 60B20

Keywords: maximum eigenvalue , Random Toeplitz matrices , Sine kernel , spectral norm

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 6 • November 2013
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