  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.
