Bárány, I;
Hug, D;
Reitzner, M;
Schneider, R;
(2017)
Random points in halfspheres.
Random Structures & Algorithms
, 50
(1)
pp. 3-22.
10.1002/rsa.20644.
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Abstract
A random spherical polytope Pn in a spherically convex set inline image as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of Pn 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 Pn, 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.
| Type: | Article |
|---|---|
| Title: | Random points in halfspheres |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1002/rsa.20644 |
| Publisher version: | http://dx.doi.org/10.1002/rsa.20644 |
| Language: | English |
| Additional information: | This is the peer reviewed version of the following article: Bárány, I; Hug, D; Reitzner, M; Schneider, R; (2017) Random points in halfspheres. Random Structures & Algorithms, 50 (1) pp. 3-22, which has been published in final form at: http://dx.doi.org/10.1002/rsa.20644. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving (http://olabout.wiley.com/WileyCDA/Section/id-828039.html#terms). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1503478 |
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