Regularity Conditions for Convergence of Linear Statistics of GUE

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.

Preliminary version. Previous version included an incorrect argument for general Wigner matrices, which is withdrawn

References in corpus (2)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices

Cited by in corpus (4)

• Fluctuations Of Linear Spectral Statistics Of Deformed Wigner Matrices
• The Common Limit of the Linear Statistics of Zeros of Random Polynomials and Their Derivatives
• Symmetric Function Theory and Unitary Invariant Ensembles
• Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices