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

Sergey Berezin (1) , Alexander I. Bufetov (1)

1 I2M - Institut de Mathématiques de Marseille

Under the Kolmogorov-Smirnov metric, an upper bound for the rate of convergence to the Gaussian law is obtained for linear statistics of matrix ensembles corresponding to Gaussian, Laguerre, and Jacobi weights. The main lemma, obtained by an analysis of the corresponding Riemann-Hilbert problem, is a uniform estimate for the characteristic function of our linear statistic over a growing interval.

Domaines: Mathématiques [math]; Physique mathématique [math-ph]; Probabilités [math.PR]

Sergey Berezin, Alexander I. Bufetov. On the Rate of Convergence in the Central Limit Theorem for Linear Statistics of Gaussian, Laguerre, and Jacobi Ensembles. 2019. ⟨hal-02110534⟩