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Interaction of Poisson hyperplane processes and convex bodies

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  11 December 2019

Rolf Schneider
Rolf Schneider*
Affiliation:
Albert-Ludwigs-Universität
*
* Postal address: Mathematisches Institut, Albert-Ludwigs-Universität, D-79104 Freiburg im Breisgau, Germany.
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Abstract

Given a stationary and isotropic Poisson hyperplane process and a convex body K in ${\mathbb R}^d$, we consider the random polytope defined by the intersection of all closed half-spaces containing K that are bounded by hyperplanes of the process not intersecting K. We investigate how well the expected mean width of this random polytope approximates the mean width of K if the intensity of the hyperplane process tends to infinity.

Keywords

Poisson hyperplane processconvex bodymean widthapproximation

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A27: Approximation by convex sets

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 4 , December 2019 , pp. 1020 - 1032
Copyright
© Applied Probability Trust 2019 

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