A Quantitative Central Limit Theorem for Linear Statistics of Random Matrix Eigenvalues

Christian Döbler () and Michael Stolz ()
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Christian Döbler: Ruhr-Universität Bochum
Michael Stolz: Ruhr-Universität Bochum

Journal of Theoretical Probability, 2014, vol. 27, issue 3, 945-953

Abstract: 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.

Keywords: Random matrices; Haar measure; Unitary group; Speed of convergence; Central limit theorem; Traces of powers; 60F05; 60B15; 60B20 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0451-2

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