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Inequalities for the anisotropic Poisson polytope

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

J. Mecke
J. Mecke*
Affiliation:
University of Jena
*
* Postal address: Faculty for Mathematics and Informatics, University of Jena, Leutragraben 1, D-07743 Jena, Germany.
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Abstract

The typical cell of a stationary Poisson hyperplane tessellation in the d-dimensional Euclidean space is called the Poisson polytope, and the cell containing the origin is called the Poisson 0-polytope. The intention of the paper is to show that the cells of the anisotropic tessellations are in some sense larger than those of the isotropic tessellations. Under the condition of equal intensities, it is proved that the moments of order n = 1, 2, … for the volume of the Poisson 0-polytope in the anisotropic case are not smaller than the corresponding moments in the isotropic case. Similar results are derived for the Poisson polytope. Finally, generalizations are mentioned.

Keywords

LINE PROCESSHYPERPLANE PROCESSRANDOM TESSELLATIONTYPICAL CELLO-CELLPOISSON POLYGON

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 56 - 62
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

The original version of this paper was presented at the International Workshop on Stochastic Geometry, Stereology and Image Analysis held at the Universidad Internacional Menendez Pelayo, Valencia, Spain on 21–24 September 1993.

References

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