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

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.

arXiv comment45 pages, 5 figures. Final version. Cleared up exposition, added new section "Outline of proof and discussion", fixed minor typos

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Cited by in corpus (3)

• Quantitative CLT for linear eigenvalue statistics of Wigner matrices
• Speed of convergence in the Central Limit Theorem for the determinantal point process with the Bessel kernel
• Symmetric Function Theory and Unitary Invariant Ensembles