[{"quality_controlled":0,"_id":"2418","author":[{"first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","last_name":"Wagner","full_name":"Uli Wagner","orcid":"0000-0002-1494-0568"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}],"page":"50 - 56","conference":{"name":"SCG: Symposium on Computational Geometry"},"type":"conference","day":"01","date_published":"2000-06-01T00:00:00Z","year":"2000","month":"06","citation":{"apa":"Wagner, U., & Welzl, E. (2000). Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem (pp. 50–56). Presented at the SCG: Symposium on Computational Geometry, ACM. https://doi.org/10.1145/336154.336176","chicago":"Wagner, Uli, and Emo Welzl. “Origin-Embracing Distributions or a Continuous Analogue of the Upper Bound Theorem,” 50–56. ACM, 2000. https://doi.org/10.1145/336154.336176.","mla":"Wagner, Uli, and Emo Welzl. *Origin-Embracing Distributions or a Continuous Analogue of the Upper Bound Theorem*. ACM, 2000, pp. 50–56, doi:10.1145/336154.336176.","ista":"Wagner U, Welzl E. 2000. Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem. SCG: Symposium on Computational Geometry, 50–56.","ama":"Wagner U, Welzl E. Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem. In: ACM; 2000:50-56. doi:10.1145/336154.336176","short":"U. Wagner, E. Welzl, in:, ACM, 2000, pp. 50–56.","ieee":"U. Wagner and E. Welzl, “Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem,” presented at the SCG: Symposium on Computational Geometry, 2000, pp. 50–56."},"date_created":"2018-12-11T11:57:33Z","date_updated":"2021-01-12T06:57:22Z","abstract":[{"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.","lang":"eng"}],"status":"public","publisher":"ACM","doi":"10.1145/336154.336176","publication_status":"published","extern":1,"title":"Origin-embracing distributions or a continuous analogue of the Upper Bound Theorem","publist_id":"4507"}]