Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 46, Number 4 (2014), 919-936.
Approximation properties of random polytopes associated with Poisson hyperplane processes
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.
Adv. in Appl. Probab., Volume 46, Number 4 (2014), 919-936.
First available in Project Euclid: 12 December 2014
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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. https://projecteuclid.org/euclid.aap/1418396237