Brillinger mixing of determinantal point processes and statistical applications

TL;DR

This paper proves that stationary determinantal point processes are Brillinger mixing, enabling the derivation of a central limit theorem which supports asymptotic statistical inference for these processes.

Contribution

It establishes Brillinger mixing for stationary determinantal point processes and derives a central limit theorem for key functionals, advancing statistical analysis methods.

Findings

Proved Brillinger mixing property for stationary determinantal point processes

Established a central limit theorem for functionals of these processes

Demonstrated asymptotic normality of intensity and kernel estimators

Abstract

Stationary determinantal point processes are proved to be Brillinger mixing. This property is an important step towards asymptotic statistics for these processes. As an important example, a central limit theorem for a wide class of functionals of determinantal point processes is established. This result yields in particular the asymptotic normality of the estimator of the intensity of a stationary determinantal point process and of the kernel estimator of its pair correlation.