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1. CMB 2010 (vol 53 pp. 614)

Böröczky, Károly J.; Schneider, Rolf
 The Mean Width of Circumscribed Random Polytopes For a given convex body \$K\$ in \${\mathbb R}^d\$, a random polytope \$K^{(n)}\$ is defined (essentially) as the intersection of \$n\$ independent closed halfspaces containing \$K\$ and having an isotropic and (in a specified sense) uniform distribution. We prove upper and lower bounds of optimal orders for the difference of the mean widths of \$K^{(n)}\$ and \$K\$ as \$n\$ tends to infinity. For a simplicial polytope \$P\$, a precise asymptotic formula for the difference of the mean widths of \$P^{(n)}\$ and \$P\$ is obtained. Keywords:random polytope, mean width, approximationCategories:52A22, 60D05, 52A27

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