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Stochastical approximation of convex bodies. (English) Zbl 0543.52003
The convex hull of n points chosen independently and uniformly at random from the boundary of a d-dimensional convex body C is a random polytope approximating C. The expected surface area, the expected mean width and the expected number of facets of this polytope are explicitly derived if C is a ball. Further, the asymptotic behaviour (\(n\to \infty)\) of the expected mean width is determined in the case that C is an arbitrary sufficiently smooth convex body.

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