Approximation properties of random polytopes associated with Poisson hyperplane processes

Daniel Hug; Rolf Schneider

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arXiv · 1309.3989

Approximation properties of random polytopes associated with Poisson hyperplane processes

Daniel Hug·Rolf Schneider

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Abstract

We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection of all closed halfspaces bounded by hyperplanes of the process and containing $K$. We study how well these random polytopes approximate $K$ (measured by the Hausdorff distance) if the intensity increases, and how this approximation depends on the directional distribution in relation to properties of $K$.

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Daniel Hug, Rolf Schneider. 2013-09-16. Approximation properties of random polytopes associated with Poisson hyperplane processes. https://arxiv.org/abs/1309.3989

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