Brillinger mixing of determinantal point processes and statistical applications

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.