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Interaction of Poisson hyperplane processes and convex bodies

Published online by Cambridge University Press:  11 December 2019

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

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.

Type
Research Papers
Copyright
© Applied Probability Trust 2019 

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