A quantitative central limit theorem for linear statistics of random matrix eigenvalues

Christian Döbler; Michael Stolz

doi:10.1007/s10959-012-0451-2

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arXiv · 1205.5403

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

Christian Döbler·Michael Stolz

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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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Christian Döbler, Michael Stolz. 2012-09-24. A quantitative central limit theorem for linear statistics of random matrix eigenvalues. https://doi.org/10.1007/s10959-012-0451-2

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