Poisson approximation with applications to stochastic geometry

This article compares the distributions of integer-valued random variables and Poisson variables. It considers total variation Wasserstein distance provides, in particular, explicit bounds on pointwise difference between cumulative distribution functions. Special attention is dedicated to estimating when functions are evaluated at 0. permits approximate minimum (or maximum) a collection by suitable variable Kolmogorov distance. The main theoretical results obtained combining Chen-Stein method with size-bias coupling generalization for developed herein. A wide variety applications then discussed focus stochastic geometry. In transforms minimal circumscribed radius maximal inradius Poisson-Voronoi tessellations as well inter-point points process considered their distances extreme value derived.