Mesoscopic eigenvalue statistics of wigner matrices

Authors
He, Yukun Knowles, Antti
Citation
He, Yukun et Knowles, Antti, Mesoscopic eigenvalue statistics of wigner matrices, Annals of applied probability , 27(3), 2017, pp. 1510-1550
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
27
Issue
3
Year of publication
2017
Pages
1510 - 1550
Database
ACNP
SICI code
Abstract
We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, that is, scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.