Interaction of Poisson hyperplane processes and convex bodies

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 halfspaces 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.

13 pages

References in corpus (3)

• Poisson polytopes
• Central limit theorems for uniform model random polygons
• The volume of random polytopes circumscribed around a convex body