A quantitative central limit theorem for linear statistics of random matrix eigenvalues
Probability
2012-09-25 v2 Mathematical Physics
math.MP
Abstract
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.
Cite
@article{arxiv.1205.5403,
title = {A quantitative central limit theorem for linear statistics of random matrix eigenvalues},
author = {Christian Döbler and Michael Stolz},
journal= {arXiv preprint arXiv:1205.5403},
year = {2012}
}
Comments
Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probability