Local convergence of the Boolean shell model towards the thick Poisson hyperplane process in the Euclidean space

Abstract

In this article we prove local convergence for a Boolean model of shells conditioned by the noncovering of the origin towards the thick hyperplane Poisson process in the Euclidean space. The existing results of Hall as well as the convergence theorems proved by Paroux or Molchanov concerned the zero-width process and the connected component of the unfilled region of the origin. Our results deal with the convergence in any given window of the space, with the earlier results of Paroux and Molchanov as a corollary.