The Mean Width of Circumscribed Random Polytopes

Canadian mathematical bulletin

Károly J. Böröczky²  Rolf Schneider¹ 

[1] Mathematisches Institut, Albert-Ludwigs-Universität, Freiburg i. Br., Germany;Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

关键词: random polytope;    mean width;    approximation;   

DOI  :  10.4153/CMB-2010-067-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 isotropicand (in a specified sense) uniform distribution. We prove upper andlower bounds of optimal orders for the difference of the mean widthsof $K^{(n)}$ and $K$ as $n$ tends to infinity. For a simplicialpolytope $P$, a precise asymptotic formula for the difference of themean widths of $P^{(n)}$ and $P$ is obtained.

【 授权许可】

Unknown