This article is cited in 3 papers

Rate of convergence in the central limit theorem for the determinantal point process with Bessel kernel

S. M. Gorbunov<sup>abc

a</sup> Landau Phystech School of Physics and Research, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia
^b Ivannikov Institute for System Programming of the Russian Academy of Science, Moscow, Russia
^c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We consider a family of linear operators diagonalized by the Hankel transform. We express explicitly the Fredholm determinants of these operators, as restricted to $L_2[0, R]$, so that the rate of their convergence as $R\to\infty$ can be found. We use the link between these determinants and the distribution of additive functionals in a determinantal point process with Bessel kernel and estimate the distance in the Kolmogorov–Smirnov metric between the distribution of these functionals and the Gaussian distribution.
Bibliography: 27 titles.

Keywords: Bessel kernel, Wiener–Hopf operators, Fredholm determinants, additive functionals.

MSC: Primary 47B35; Secondary 60G55

Received: 10.06.2024

DOI: 10.4213/sm10137

 English version: Sbornik: Mathematics, 2024, 215:12, 1607–1632

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