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