Mean width of random polytopes in a reasonably smooth convex body

K.J. Böröczky, F. Fodor, M. Reitzner and V. Vígh

Journal of Multivariate Analysis, 2009, vol. 100, issue 10, 2287-2295

Abstract: Let K be a convex body in and let Xn=(x1,...,xn) be a random sample of n independent points in K chosen according to the uniform distribution. The convex hull Kn of Xn is a random polytope in K, and we consider its mean width W(Kn). In this article, we assume that K has a rolling ball of radius [varrho]>0. First, we extend the asymptotic formula for the expectation of W(K)-W(Kn) which was earlier known only in the case when [not partial differential]K has positive Gaussian curvature. In addition, we determine the order of magnitude of the variance of W(Kn), and prove the strong law of large numbers for W(Kn). We note that the strong law of large numbers for any quermassintegral of K was only known earlier for the case when [not partial differential]K has positive Gaussian curvature.

Keywords: Random; polytope; Mean; width (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00128-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:100:y:2009:i:10:p:2287-2295

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().