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

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  22 February 2016

Julien Michel  and
Katy Paroux
Julien Michel*
Affiliation:
ENS Lyon
Katy Paroux*
Affiliation:
Université de Franche Comté
*
∗ Postal address: Unité de Mathématiques Pures et Appliquées, UMR 5669, F-69364 Lyon Cedex 07, France. Email address: [email protected]
∗∗ Postal address: Laboratoire de Mathématiques de Besançon, UMR 6623, F-25030 Besançon Cedex, France.
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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.

Keywords

Stochastic geometrypoint process

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 35 , Issue 2 , June 2003 , pp. 354 - 361
Copyright
Copyright © Applied Probability Trust 2003 

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References

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