Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem Conference Paper


Author(s): Wagner, Uli; Welzl, Emo
Title: Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem
Affiliation
Abstract: For an absolutely continuous probability measure μ on Rd and a nonnegative integer k, let sk(μ, 0) denote the probability that the convex hull of k+d+1 random points which are i.i.d. according to μ contains the origin 0. For d and k given, we determine a tight upper bound on sk(μ, 0), and we characterize the measures in Rd which attain this bound. This result can be considered a continuous analogue of the Upper Bound Theorem for the maximal number of faces of convex polytopes with a given number of vertices. For our proof we introduce so-called h-functions, continuous counterparts of h-vectors for simplicial convex polytopes.
Keywords: theorem proving; Functions; Probability distributions; Vectors
Conference Title: SCG: Symposium on Computational Geometry
Conference Dates: June 12-14, 2000
Conference Location: Hong Kong, China
Publisher: ACM  
Date Published: 2000-06-01
Start Page: 50
End Page: 56
DOI: 10.1145/336154.336176
Open access: no
IST Austria Authors
  1. Uli Wagner
    50 Wagner
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