论文标题
与快速衰减依赖性点过程的几何统计的收敛速率
Convergence rate for geometric statistics of point processes with fast decay dependence
论文作者
论文摘要
[Błaszczyszyn，Yogeshwaran和Yukich（2019）]确定了具有快速衰减依赖性点过程的几何过程中的中心限制定理。由于限制定理的使用有限，除非我们了解它们在近似中涉及的错误，否则在本文中，我们考虑了$ \ mathbb {r}^d $在满足快速衰减依赖性的$ \ mathbb {r}^d $上的点过程统计数据方面的正常近似速率。我们证明了定理用于两个点过程家族引起的统计数据：稀有的吉布斯点过程和具有快速衰减内核的确定点过程。
[Błaszczyszyn, Yogeshwaran and Yukich (2019)] established central limit theorems for geometric statistics of point processes having fast decay dependence. As limit theorems are of limited use unless we understand their errors involved in the approximation, in this paper, we consider the rates of a normal approximation in terms of the Wasserstein distance for statistics of point processes on $\mathbb{R}^d$ satisfying fast decay dependence. We demonstrate the use of the theorems for statistics arising from two families of point processes: the rarified Gibbs point processes and the determinantal point processes with fast decay kernels.
