Advances in Applied Probability

Approximation properties of random polytopes associated with Poisson hyperplane processes

Daniel Hug and Rolf Schneider

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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.

Article information

Adv. in Appl. Probab., Volume 46, Number 4 (2014), 919-936.

First available in Project Euclid: 12 December 2014

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Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Poisson hyperplane process zero polytope approximation of convex bodies directional distribution


Hug, Daniel; Schneider, Rolf. Approximation properties of random polytopes associated with Poisson hyperplane processes. Adv. in Appl. Probab. 46 (2014), no. 4, 919--936. doi:10.1239/aap/1418396237.

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