1205.5403 (Christian Döbler et al.)

Linear statistics of random matrix eigenvalues via Stein's method    [PDF]

Christian Döbler, Michael Stolz

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.

View original: http://arxiv.org/abs/1205.5403