## Approximation of smooth convex bodies by random circumscribed polytopes.(English)Zbl 1049.60009

Authors’ summary: Choose $$n$$ independent random points on the boundary of a convex body $$K\subset\mathbb{R}^d$$. The intersection of the supporting halfspaces of these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. On the case that the boundary of $$K$$ is sufficiently smooth, asymptotic expansions as $$n\to\infty$$ are derived even in the case when the curvature is allowed to be zero. We compare our results to the analogous results for best approximating polytopes.

### MSC:

 60D05 Geometric probability and stochastic geometry 52A22 Random convex sets and integral geometry (aspects of convex geometry)
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### References:

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