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Inequalities for mixed stationary Poisson hyperplane tessellations

Published online by Cambridge University Press:  01 July 2016

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.

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.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 1998 

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