---
res:
bibo_abstract:
- Using the geodesic distance on the n-dimensional sphere, we study the expected
radius function of the Delaunay mosaic of a random set of points. Specifically,
we consider the partition of the mosaic into intervals of the radius function
and determine the expected number of intervals whose radii are less than or equal
to a given threshold. We find that the expectations are essentially the same as
for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the
points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to
the boundary complex of the convex hull in Rn+1, so we also get the expected number
of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in
Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric
to the standard n-simplex equipped with the Fisher information metric. It follows
that the latter space has similar stochastic properties as the n-dimensional Euclidean
space. Our results are therefore relevant in information geometry and in population
genetics.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Edelsbrunner, Herbert
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
- foaf_Person:
foaf_givenName: Anton
foaf_name: Nikitenko, Anton
foaf_surname: Nikitenko
foaf_workInfoHomepage: http://www.librecat.org/personId=3E4FF1BA-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1214/18-AAP1389
bibo_issue: '5'
bibo_volume: 28
dct_date: 2018^xs_gYear
dct_language: eng
dct_publisher: Institute of Mathematical Statistics@
dct_title: Random inscribed polytopes have similar radius functions as Poisson-Delaunay
mosaics@
...