Regularity Conditions for Convergence of Linear Statistics of GUE
Probability
2015-10-14 v2
Abstract
We establish a central limit theorem for the unnormalized linear statistic of the Gaussian Unitary Ensemble under optimal conditions: the linear statistics converges if and only if the expression for the limiting variance is finite.
Keywords
Cite
@article{arxiv.1510.02988,
title = {Regularity Conditions for Convergence of Linear Statistics of GUE},
author = {Phil Kopel},
journal= {arXiv preprint arXiv:1510.02988},
year = {2015}
}
Comments
Preliminary version. Previous version included an incorrect argument for general Wigner matrices, which is withdrawn