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arXiv · 1808.05432

Small faces in stationary Poisson hyperplane tessellations

Rolf Schneider
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Abstract

We consider the tessellation induced by a stationary Poisson hyperplane process in $d$-dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the $k$-faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical $k$-face, under the condition of small size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.

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Rolf Schneider. 2018-08-16. Small faces in stationary Poisson hyperplane tessellations. https://arxiv.org/abs/1808.05432

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