Normal approximation for coverage models over binomial point processes

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.Comment: Published in at http://dx.doi.org/10.1214/09-AAP634 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org