English

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

Probability 2013-12-17 v2

Abstract

We show that the top eigenvalue of an n×nn\times n random symmetric Toeplitz matrix, scaled by 2nlogn\sqrt{2n\log n}, converges to the square of the 242\to4 operator norm of the sine kernel.

Keywords

Cite

@article{arxiv.1109.5494,
  title  = {The top eigenvalue of the random Toeplitz matrix and the sine kernel},
  author = {Arnab Sen and Bálint Virág},
  journal= {arXiv preprint arXiv:1109.5494},
  year   = {2013}
}

Comments

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)

R2 v1 2026-06-21T19:10:11.286Z