Convergence rate for geometric statistics of point processes having fast decay of dependence

Abstract

[BYY19] established central limit theorems for geometric statistics of point processes having fast decay of 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 of 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 kernels decaying fast enough.