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A Quantitative Central Limit Theorem for Linear Statistics of Random Matrix Eigenvalues
Authors:Christian Döbler  Michael Stolz
Institution:1. Fakult?t für Mathematik, Ruhr-Universit?t Bochum, 44780, Bochum, Germany
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 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.
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