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

Arnab Sen; Bálint Virág

doi:10.1214/13-AOP863

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

Arnab Sen, Bálint Virág

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We show that the top eigenvalue of an n × n random symmetric Toeplitz matrix, scaled by √2n log n, converges to the square of the 2 → 4 operator norm of the sine kernel.

Original language	English (US)
Pages (from-to)	4050-4079
Number of pages	30
Journal	Annals of Probability
Volume	41
Issue number	6
DOIs	https://doi.org/10.1214/13-AOP863
State	Published - Nov 2013

Keywords

Maximum eigenvalue
Random toeplitz matrices
Sine kernel
Spectral norm

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abstract = "We show that the top eigenvalue of an n × n random symmetric Toeplitz matrix, scaled by √2n log n, converges to the square of the 2 → 4 operator norm of the sine kernel.",

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KW - Maximum eigenvalue

KW - Random toeplitz matrices

KW - Sine kernel

KW - Spectral norm

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

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Keywords

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