Global spectral fluctuations in the Gaussian Unitary Ensemble
Probability
2015-10-21 v1 Mathematical Physics
math.MP
Abstract
We consider global fluctuations of the spectrum of the GUE. Using results on the linear statistics of such matrices as well as variance bounds on the eigenvalues, we show that under a suitable scaling, global fluctuations of the spectrum can be asymptotically described in terms of a logarithmically correlated Gaussian field. We also discuss briefly connections between different objects in RMT giving rise to log-correlated fields: the logarithm of the absolute value of the characteristic polynomial, the eigenvalue counting function, and the field of fluctuations of the eigenvalues around their expected locations.
Keywords
Cite
@article{arxiv.1510.05867,
title = {Global spectral fluctuations in the Gaussian Unitary Ensemble},
author = {Christian Webb},
journal= {arXiv preprint arXiv:1510.05867},
year = {2015}
}