Geodesic
Rate of convergence in the central limit theorem for the determinantal point process with Bessel kernel
Sbornik. Mathematics, Tome 215 (2024) no. 12, pp. 1607-1632

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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: Wiener–Hopf operators, Fredholm determinants, additive functionals.
Mots-clés : Bessel kernel 
@article{SM_2024_215_12_a1,
     author = {S. M. Gorbunov},
     title = {Rate of convergence in the central limit theorem for the determinantal point process with {Bessel} kernel},
     journal = {Sbornik. Mathematics},
     pages = {1607--1632},
     publisher = {mathdoc},
     volume = {215},
     number = {12},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_12_a1/}
}
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S. M. Gorbunov. Rate of convergence in the central limit theorem for the determinantal point process with Bessel kernel. Sbornik. Mathematics, Tome 215 (2024) no. 12, pp. 1607-1632. http://geodesic.mathdoc.fr/item/SM_2024_215_12_a1/