---
_id: '2418'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
author:
- first_name: Uli
  full_name: Wagner, Uli
  id: 36690CA2-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
  orcid: 0000-0002-1494-0568
- first_name: Emo
  full_name: Welzl, Emo
  last_name: Welzl
citation:
  ama: 'Wagner U, Welzl E. Origin-embracing distributions or a continuous analogue
    of the Upper Bound Theorem. In: <i>Proceedings of the 16th Annual Symposium on
    Computational Geometry</i>. ACM; 2000:50-56. doi:<a href="https://doi.org/10.1145/336154.336176">10.1145/336154.336176</a>'
  apa: 'Wagner, U., &#38; Welzl, E. (2000). Origin-embracing distributions or a continuous
    analogue of the Upper Bound Theorem. In <i>Proceedings of the 16th annual symposium
    on Computational geometry</i> (pp. 50–56). Clear Water Bay Kowloon, Hong Kong:
    ACM. <a href="https://doi.org/10.1145/336154.336176">https://doi.org/10.1145/336154.336176</a>'
  chicago: Wagner, Uli, and Emo Welzl. “Origin-Embracing Distributions or a Continuous
    Analogue of the Upper Bound Theorem.” In <i>Proceedings of the 16th Annual Symposium
    on Computational Geometry</i>, 50–56. ACM, 2000. <a href="https://doi.org/10.1145/336154.336176">https://doi.org/10.1145/336154.336176</a>.
  ieee: U. Wagner and E. Welzl, “Origin-embracing distributions or a continuous analogue
    of the Upper Bound Theorem,” in <i>Proceedings of the 16th annual symposium on
    Computational geometry</i>, Clear Water Bay Kowloon, Hong Kong, 2000, pp. 50–56.
  ista: 'Wagner U, Welzl E. 2000. Origin-embracing distributions or a continuous analogue
    of the Upper Bound Theorem. Proceedings of the 16th annual symposium on Computational
    geometry. SCG: Symposium on Computational Geometry, 50–56.'
  mla: Wagner, Uli, and Emo Welzl. “Origin-Embracing Distributions or a Continuous
    Analogue of the Upper Bound Theorem.” <i>Proceedings of the 16th Annual Symposium
    on Computational Geometry</i>, ACM, 2000, pp. 50–56, doi:<a href="https://doi.org/10.1145/336154.336176">10.1145/336154.336176</a>.
  short: U. Wagner, E. Welzl, in:, Proceedings of the 16th Annual Symposium on Computational
    Geometry, ACM, 2000, pp. 50–56.
conference:
  end_date: 2000-04-14
  location: Clear Water Bay Kowloon, Hong Kong
  name: 'SCG: Symposium on Computational Geometry'
  start_date: 2000-06-12
date_created: 2018-12-11T11:57:33Z
date_published: 2000-05-01T00:00:00Z
date_updated: 2023-05-03T12:41:02Z
day: '01'
doi: 10.1145/336154.336176
extern: '1'
language:
- iso: eng
month: '05'
oa_version: None
page: 50 - 56
publication: Proceedings of the 16th annual symposium on Computational geometry
publication_identifier:
  isbn:
  - '9781581132243'
publication_status: published
publisher: ACM
publist_id: '4507'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Origin-embracing distributions or a continuous analogue of the Upper Bound
  Theorem
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '2000'
...