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arXiv · 1609.04230

On the cells in a stationary Poisson hyperplane mosaic

Matthias Reitzner·Rolf Schneider
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Abstract

Let $X$ be the mosaic generated by a stationary Poisson hyperplane process $\hat X$ in ${\mathbb R}^d$. Under some mild conditions on the spherical directional distribution of $\hat X$ (which are satisfied, for example, if the process is isotropic), we show that with probability one the set of cells ($d$-polytopes) of $X$ has the following properties. The translates of the cells are dense in the space of convex bodies. Every combinatorial type of simple $d$-polytopes is realized infinitely often by the cells of $X$. A further result concerns the distribution of the typical cell.

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Matthias Reitzner, Rolf Schneider. 2016-09-14. On the cells in a stationary Poisson hyperplane mosaic. https://arxiv.org/abs/1609.04230

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