The top eigenvalue of the random Toeplitz matrix and the sine kernel

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 $2\to 4$ operator norm of the sine kernel.

Published in at http://dx.doi.org/10.1214/13-AOP863 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• A simple invariance theorem

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