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

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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.

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