Local convergence of the boolean shell model towards the thick poisson hyperplane process in the euclidean space

in this article we prove local convergence for a Boolean model of shells conditioned hv the noncovering of the origin towards the thick hyperplane Poison 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 unfiled region of the origin. Our results deal with the convergence in any enem window of the space, with the earlier results of Paroux and Molchanov as a corollary.