Geodesic
The Mean Width of Circumscribed Random Polytopes
Canadian mathematical bulletin, Tome 53 (2010) no. 4, pp. 614-628

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DOI

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.
DOI : 10.4153/CMB-2010-067-5
Mots-clés : 52A22, 60D05, 52A27, random polytope, mean width, approximation 
Böröczky, Károly J.; Schneider, Rolf. The Mean Width of Circumscribed Random Polytopes. Canadian mathematical bulletin, Tome 53 (2010) no. 4, pp. 614-628. doi: 10.4153/CMB-2010-067-5
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     author = {B\"or\"oczky, K\'aroly J. and Schneider, Rolf},
     title = {The {Mean} {Width} of {Circumscribed} {Random} {Polytopes}},
     journal = {Canadian mathematical bulletin},
     pages = {614--628},
     year = {2010},
     volume = {53},
     number = {4},
     doi = {10.4153/CMB-2010-067-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-067-5/}
}
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