Regularity Conditions for Convergence of Linear Statistics of GUE

Phil Kopel

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arXiv · 1510.02988

Regularity Conditions for Convergence of Linear Statistics of GUE

Phil Kopel

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Abstract

We establish a central limit theorem for the unnormalized linear statistic of the Gaussian Unitary Ensemble under optimal conditions: the linear statistics converges if and only if the expression for the limiting variance is finite.

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Phil Kopel. 2015-10-13. Regularity Conditions for Convergence of Linear Statistics of GUE. https://arxiv.org/abs/1510.02988

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