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September 2014 On the volume of the zero cell of a class of isotropic Poisson hyperplane tessellations
Julia Hörrmann, Daniel Hug
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Adv. in Appl. Probab. 46(3): 622-642 (September 2014). DOI: 10.1239/aap/1409319552

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 ∞.

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Julia Hörrmann. Daniel Hug. "On the volume of the zero cell of a class of isotropic Poisson hyperplane tessellations." Adv. in Appl. Probab. 46 (3) 622 - 642, September 2014. https://doi.org/10.1239/aap/1409319552

Information

Published: September 2014
First available in Project Euclid: 29 August 2014

zbMATH: 1319.60013
MathSciNet: MR3254334
Digital Object Identifier: 10.1239/aap/1409319552

Subjects:
Primary: 60D05
Secondary: 52A22

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 3 • September 2014
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