Regularity Conditions for Convergence of Linear Statistics of GUE

2015/10/10 by Phil Kopel, Kopel, Phil
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1510.02988

openalex publication_date 2015/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices

Related

• On the Rate of Convergence in the Central Limit Theorem for Linear Statistics of Gaussian, Laguerre, and Jacobi Ensembles
• On the regularity conditions in the CLT for the LUE
• Quantitative Normal Approximation of Linear Statistics of β-ensembles
• A convergent (1)/(N) expansion for GUE
• Sharp total variation rates of convergence for fluctuations of linear statistics of β-ensembles