On a conjecture of R. E. Miles about the convex hull of random points期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On a conjecture of R. E. Miles about the convex hull of random points

Authors:	Christian Buchta

Affiliation:	(1) Mathematisches Institut der Universität, Albertstrasse 23 b, D-7800 Freiburg im Breisgau, Germany;(2) Present address: Institut für Analysis, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria

Abstract:	Denoty byp_d+i(B_d,d+m) the probability that the convex hull ofd+m points chosen independently and uniformly from ad-dimensional ballB_d possessesd+i(i=1,...,m) vertices. We prove Mile's conjecture that, given any integerm, p_d+m(B_d,d+m)»1 asd». This is obvious form=1 and was shown by Kingman form=2 and by Miles form=3. Further, a related result by Miles is generalized, and several consequences are deduced.Dedicated to Professor E. Halwaka on the occasion of his seventieth

Keywords:
本文献已被 SpringerLink 等数据库收录！