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On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  22 February 2016

Julia Hörrmann  and
Daniel Hug
Julia Hörrmann*
Affiliation:
Karlsruhe Institute of Technology
Daniel Hug*
Affiliation:
Karlsruhe Institute of Technology
*
∗ Postal address: Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany.
∗ Postal address: Department of Mathematics, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany.
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Abstract

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We study a parametric class of isotropic but not necessarily stationary Poisson hyperplane tessellations in n-dimensional Euclidean space. Our focus is on the volume of the zero cell, i.e. the cell containing the origin. As a main result, we obtain an explicit formula for the variance of the volume of the zero cell in arbitrary dimensions. From this formula we deduce the asymptotic behaviour of the volume of the zero cell as the dimension goes to ∞.

Keywords

Poisson hyperplane tessellationPoisson-Voronoi tessellationzero celltypical cellvariancehigh dimensions

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 46 , Issue 3 , September 2014 , pp. 622 - 642
Copyright
© Applied Probability Trust 

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