%0 Journal Article
%T A quantitative central limit theorem for linear statistics of random matrix eigenvalues
%A Christian D£¿bler
%A Michael Stolz
%J Mathematics
%D 2012
%I arXiv
%R 10.1007/s10959-012-0451-2
%X 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 $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.
%U http://arxiv.org/abs/1205.5403v2