---
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
    orcid: 0000-0002-0659-3201
  bibo_doi: 10.1214/18-AAP1389
  bibo_issue: '5'
  bibo_volume: 28
  dct_date: 2018^xs_gYear
  dct_identifier:
  - UT:000442893500018
  dct_language: eng
  dct_publisher: Institute of Mathematical Statistics@
  dct_title: Random inscribed polytopes have similar radius functions as Poisson-Delaunay
    mosaics@
...