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Weighted faces of Poisson hyperplane tessellations

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Rolf Schneider
Rolf Schneider*
Affiliation:
Albert-Ludwigs-Universität Freiburg
*
∗ Postal address: Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstr. 1, D-79104 Freiburg, Germany. Email address: rolf.schneider@math.uni-freiburg.de
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Abstract

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We study lower-dimensional volume-weighted typical faces of a stationary Poisson hyperplane tessellation in d-dimensional Euclidean space. After showing how their distribution can be derived from that of the zero cell, we obtain sharp lower and upper bounds for the expected vertex number of the volume-weighted typical k-face (k=2,…,d). The bounds are respectively attained by parallel mosaics and by isotropic tessellations. We conclude with a remark on expected face numbers and expected intrinsic volumes of the zero cell.

Keywords

Poisson hyperplane tessellationvolume-weighted typical facePalm distributionextremal vertex numberparallel mosaicassociated zonoidvolume product

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 41 , Issue 3 , September 2009 , pp. 682 - 694
Copyright
Copyright © Applied Probability Trust 2009 

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