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arXiv · 1010.2333

Large faces in Poisson hyperplane mosaics

Daniel Hug·Rolf Schneider
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Abstract

A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in ${\mathbb{R}}^d$, under the condition that it has large volume, approximates with high probability a certain definite shape, which is determined by the directional distribution of the underlying hyperplane process. This result is extended here to typical $k$-faces of the tessellation, for $k\in\{2,...,d-1\}$. This requires the additional condition that the direction of the face be in a sufficiently small neighbourhood of a given direction.

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Daniel Hug, Rolf Schneider. 2010-10-12. Large faces in Poisson hyperplane mosaics. https://doi.org/10.1214/09-aop510

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