Central limit theorem for the determinantal point process with the confluent hypergeometric kernel

TL;DR

This paper proves that additive functionals of a determinantal point process with a confluent hypergeometric kernel converge to a Gaussian distribution as the scale parameter grows, providing explicit error estimates.

Contribution

It establishes a central limit theorem for these functionals and derives an exact Fredholm determinant identity for their expectations.

Findings

Additive functionals approach Gaussian distribution as R→∞

Explicit Kolmogorov-Smirnov distance estimates provided

Derived an exact identity for expectations of multiplicative functionals

Abstract

We consider the convergence of additive functionals under the determinantal point process with the confluent hypergeometric kernel, corresponding to a sufficiently smooth function $f(x/R)$, as $R\to\infty$. We show that these functionals approach Gaussian distribution and give an estimate on the Kolmogorov-Smirnov distance. To obtain these results, we derive an exact identity for expectations of multiplicative functionals in terms of Fredholm determinants.