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- Title
APPROXIMATION PROPERTIES OF RANDOM POLYTOPES ASSOCIATED WITH POISSON HYPERPLANE PROCESSES.
- Authors
HUG, DANIEL; SCHNEIDER, ROLF
- 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.
- Subjects
APPROXIMATION theory; POLYTOPES; HYPERPLANES; EUCLIDEAN domains; TOPOLOGY
- Publication
Advances in Applied Probability, 2014, Vol 46, Issue 4, p919
- ISSN
0001-8678
- Publication type
Article
- DOI
10.1239/aap/1418396237