location:  Publications → journals → CMB
Abstract view

# The Mean Width of Circumscribed Random Polytopes

Published:2010-07-26
Printed: Dec 2010
• Károly J. Böröczky,
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary
• Rolf Schneider,
Mathematisches Institut, Albert-Ludwigs-Universität, Freiburg i. Br., Germany
 Format: HTML LaTeX MathJax PDF

## Abstract

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
 MSC Classifications: 52A22 - Random convex sets and integral geometry [See also 53C65, 60D05] 60D05 - Geometric probability and stochastic geometry [See also 52A22, 53C65] 52A27 - Approximation by convex sets

 top of page | contact us | privacy | site map |