Advances in Applied Probability

On the volume of the zero cell of a class of isotropic Poisson hyperplane tessellations

Julia Hörrmann and Daniel Hug

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Abstract

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 ∞.

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 3 (2014), 622-642.

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1409319552

Digital Object Identifier
doi:10.1239/aap/1409319552

Mathematical Reviews number (MathSciNet)
MR3254334

Zentralblatt MATH identifier
1319.60013

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 52A22: Random convex sets and integral geometry [See also 53C65, 60D05]

Keywords
Poisson hyperplane tessellation Poisson-Voronoi tessellation zero cell typical cell variance high dimensions

Citation

Hörrmann, Julia; Hug, Daniel. On the volume of the zero cell of a class of isotropic Poisson hyperplane tessellations. Adv. in Appl. Probab. 46 (2014), no. 3, 622--642. doi:10.1239/aap/1409319552. https://projecteuclid.org/euclid.aap/1409319552


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