Intersections of random sets

Abstract

We consider a variant of a classical coverage process, the boolean model in ${\mathbb{R}}^d$. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well studied limit $C$. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original boolean model, we show that the scaled intersection converges weakly to the same limit $C$. Along the way, we present some tools for studying statistics of a class of intersection models.

28 pages, 4 figures

References in corpus (1)

• Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius