Random Points in Halfspheres
Autor(en): | Barany, Imre Hug, Daniel Reitzner, Matthias Schneider, Rolf |
Stichwörter: | (spherical) surface area, volume and mean width; APPROXIMATION; Computer Science; Computer Science, Software Engineering; CONVEX HULLS; face numbers; Hausdorff distance; Mathematics; Mathematics, Applied; RANDOM POLYTOPES; random polytopes in halfspheres; spherical spaces | Erscheinungsdatum: | 2017 | Herausgeber: | WILEY | Journal: | RANDOM STRUCTURES & ALGORITHMS | Volumen: | 50 | Ausgabe: | 1 | Startseite: | 3 | Seitenende: | 22 | Zusammenfassung: | A random spherical polytope P-n in a spherically convex set K subset of S-d as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of P-n for a spherically convex set K contained in an open halfsphere is quite similar to that of a similarly generated random convex polytope in a Euclidean space, but the case when K is a halfsphere is different. This is what we investigate here, establishing the asymptotic behaviour, as n tends to infinity, of the expectation of several characteristics of P-n, such as facet and vertex number, volume and surface area. For the Hausdorff distance from the halfsphere, we obtain also some almost sure asymptotic estimates. (C) 2016 Wiley Periodicals, Inc. |
ISSN: | 10429832 | DOI: | 10.1002/rsa.20644 |
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geprüft am 17.05.2024