---
res:
bibo_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.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Uli
foaf_name: Uli Wagner
foaf_surname: Wagner
foaf_workInfoHomepage: http://www.librecat.org/personId=36690CA2-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-1494-0568
- foaf_Person:
foaf_givenName: Emo
foaf_name: Welzl, Emo
foaf_surname: Welzl
bibo_doi: 10.1145/336154.336176
dct_date: 2000^xs_gYear
dct_publisher: ACM@
dct_title: Origin-embracing distributions or a continuous analogue of the Upper
Bound Theorem@
...