Monatshefte für Mathematik

, Volume 102, Issue 2, pp 91–102

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

  • Christian Buchta
Article

DOI: 10.1007/BF01490202

Cite this article as:
Buchta, C. Monatshefte für Mathematik (1986) 102: 91. doi:10.1007/BF01490202

Abstract

Denoty bypd+i(Bd,d+m) the probability that the convex hull ofd+m points chosen independently and uniformly from ad-dimensional ballBd possessesd+i(i=1,...,m) vertices. We prove Mile's conjecture that, given any integerm, pd+m(Bd,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.

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Christian Buchta
    • 1
  1. 1.Mathematisches Institut der UniversitätFreiburg im BreisgauGermany
  2. 2.Institut für AnalysisTechnische Universität WienWienAustria