Speed of convergence in the Central Limit Theorem for the determinantal point process with the Bessel kernel

Abstract

We consider a family of linear operators, diagonalized by the Hankel transform. The Fredholm determinants of these operators, restricted to $L_2[0,R]$, are expressed in a convenient form for asymptotic analysis as $R\to \infty$. The result is an identity, in which the determinant is equal to the leading asymptotic multiplied by an asymptotically small factor, for which an explicit formula is derived. We apply the result to the determinantal point process with the Bessel kernel, calculating the speed of the convergence of additive functionals with respect to the Kolmogorov-Smirnov metric.

arXiv comment25 pages; corrected proof of Corollary 8.2 and the definition of Wiener-Hopf operator on page 3

References in corpus (8)

• Determinantal random point fields
• Level-Spacing Distributions and the Bessel Kernel
• Rate of convergence of linear functions on the unitary group
• Asymptotics of determinants of Bessel operators
• Correlations for symplectic and orthogonal Schur measures
• On the Rate of Convergence in the Central Limit Theorem for Linear Statistics of Gaussian, Laguerre, and Jacobi Ensembles
• The sine-process has excess one
• Quantitative CLT for linear eigenvalue statistics of Wigner matrices