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- Title
Spherical convex hull of random points on a wedge.
- Authors
Besau, Florian; Gusakova, Anna; Reitzner, Matthias; Schütt, Carsten; Thäle, Christoph; Werner, Elisabeth M.
- Abstract
Consider two half-spaces H 1 + and H 2 + in R d + 1 whose bounding hyperplanes H 1 and H 2 are orthogonal and pass through the origin. The intersection S 2 , + d : = S d ∩ H 1 + ∩ H 2 + is a spherical convex subset of the d-dimensional unit sphere S d , which contains a great subsphere of dimension d - 2 and is called a spherical wedge. Choose n independent random points uniformly at random on S 2 , + d and consider the expected facet number of the spherical convex hull of these points. It is shown that, up to terms of lower order, this expectation grows like a constant multiple of log n . A similar behaviour is obtained for the expected facet number of a homogeneous Poisson point process on S 2 , + d . The result is compared to the corresponding behaviour of classical Euclidean random polytopes and of spherical random polytopes on a half-sphere.
- Subjects
POISSON processes; WEDGES; POINT processes; POLYTOPES; HYPERPLANES; CONVEX bodies
- Publication
Mathematische Annalen, 2024, Vol 389, Issue 3, p2289
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02704-9