On the Rate of Convergence in the Central Limit Theorem for Linear Statistics of Gaussian, Laguerre, and Jacobi Ensembles

2019/04/22 by Sergey Berezin, Berezin, Sergey, Alexander I. Bufetov +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1904.09685

openalex publication_date 2019/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under the Kolmogorov--Smirnov metric, an upper bound on the rate of convergence to the Gaussian distribution is obtained for linear statistics of the matrix ensembles in the case of the Gaussian, Laguerre, and Jacobi weights. The main lemma gives an estimate for the characteristic functions of the linear statistics; this estimate is uniform over the growing interval. The proof of the lemma relies on the Riemann--Hilbert approach.

Citations

• Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight

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• Quenched properties of the Spectral Form Factor

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