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.
"Brillinger mixing of determinantal point processes and statistical applications." Electron. J. Statist. 10 (1) 582 - 607, 2016. https://doi.org/10.1214/16-EJS1116