Normal approximation for coverage models over binomial point processes

TL;DR

This paper establishes optimal convergence rates in the central limit theorem for coverage models over binomial point processes, focusing on covered volume and isolated shapes, using Stein's method for error bounds.

Contribution

It provides the first explicit error bounds demonstrating optimal convergence rates in the CLT for germ-grain coverage models with fixed radius.

Findings

Optimal error bounds for CLT in coverage models

Convergence rates for covered volume and isolated shapes

Application of Stein's method via size-biased couplings

Abstract

We give error bounds which demonstrate optimal rates of convergence in the CLT for the total covered volume and the number of isolated shapes, for germ-grain models with fixed grain radius over a binomial point process of $n$ points in a toroidal spatial region of volume $n$. The proof is based on Stein's method via size-biased couplings.