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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, approximation
Categories:52A22, 60D05, 52A27

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