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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
##### Keywords:
convex hull; random polytope
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##### References:
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