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On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations
Published online by Cambridge University Press: 22 February 2016
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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- Stochastic Geometry and Statistical Applications
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- © Applied Probability Trust
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