Random points in halfspheres

A random spherical polytope Pn in a spherically convex set K⊂Sd 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. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 3–22, 2017

• Publication year

  2015

• Venue

  Random Struct. Algorithms

• Publication date

  2015-05-18

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1002/rsa.20644arXiv 1505.04672
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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