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Inequalities for mixed stationary Poisson hyperplane tessellations

Part of:Geometric probability and stochastic geometryGeneral convexity

Published online by Cambridge University Press:  01 July 2016

J. Mecke
J. Mecke*
Affiliation:
University of Jena
*
∗ Postal address: Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, Institut für Stochastik, Ernst-Abbe Pl. 1-4, D-07743 Jena, Germany.
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Abstract

Mixings of stationary Poisson hyperplane tessellations in d-dimensional Euclidean space are considered. The intention of the paper is to show that the 0-cell of a mixed stationary Poisson hyperplane tessellation Y is in some sense larger than that of stationary Poisson hyperplane tessellations Y' with the same intensity and directional distribution as Y. Related results concerning the moments for the volume of the 0-cell are derived. In special cases, similar statements with respect to the typical cell are proved.

Keywords

Hyperplane processhyperplane tessellation0-celltypical cellvertex intensityPoisson processCox process

MSC classification

Primary:60D05: Geometric probability and stochastic geometry
Secondary:52A22: Random convex sets and integral geometry

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 4 , December 1998, pp. 921 - 928
Copyright
Copyright © Applied Probability Trust 1998 

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