Choose $n$ independent random points on the boundary of a convex
body $K \subset \R^d$. The intersection of the supporting halfspaces
at these random points is a random convex polyhedron. The expectations
of its volume, its surface area and its mean width are investigated.
In the case that the boundary of $K$ is sufficiently smooth, asymptotic
expansions as $n \to \infty$ are derived even in the case when the
curvature is allowed to be zero. We compare our results to the analogous
results for best approximating
polytopes.
Publié le : 2004-02-14
Classification:
Random approximation,
convex bodies,
circumscribed polytopes,
60D05,
52A22
@article{1075828053,
author = {B\"or\"oczky, K\'aroly and Reitzner, Matthias},
title = {Approximation of smooth convex bodies by random circumscribed polytopes},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 239-273},
language = {en},
url = {http://dml.mathdoc.fr/item/1075828053}
}
Böröczky, Károly; Reitzner, Matthias. Approximation of smooth convex bodies by random circumscribed polytopes. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 239-273. http://gdmltest.u-ga.fr/item/1075828053/