标题： 行列式点过程的Brillinger混合及统计应用 显示英文标题

标题： Brillinger mixing of determinantal point processes and statistical applications

摘要： 平稳的行列式点过程被证明是Brillinger混合的。 这一性质是这些过程渐近统计学的重要一步。 作为一个重要例子，建立了行列式点过程广泛类别的泛函的中心极限定理。 该结果特别给出了平稳行列式点过程强度估计量和其对相关函数核估计量的渐近正态性。 显示英文摘要

摘要： 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.