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

Authors
Sen, Arnab Virág, Bálint
Citation
Sen, Arnab et Virág, Bálint, The top eigenvalue of the random Toeplitz matrix and the sine kernel, Annals of probability , 41(6), 2013, pp. 4050-4079
Journal title
Annals of probability → ACNP
ISSN journal
00911798
Volume
41
Issue
6
Year of publication
2013
Pages
4050 - 4079
Database
ACNP
SICI code
Abstract
We show that the top eigenvalue of an n.n random symmetric Toeplitz matrix, scaled by .2nlogn, converges to the square of the 2.4 operator norm of the sine kernel.