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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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

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

First available in Project Euclid: 29 August 2014

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Zentralblatt MATH identifier

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

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


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.

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