Random inscribed polytopes in projective geometries
Abstract
We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation of dual volumes and the mean width of random polyhedral sets are obtained. We deduce these results by proving a general central limit theorem for the weighted volume of the convex hull of random points chosen from the boundary of a smooth convex body according to a positive and continuous density in Euclidean space. In the background are geometric estimates for weighted surface bodies and BerryEsseen bounds for functionals of independent random variables.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 arXiv:
 arXiv:2005.10502
 Bibcode:
 2020arXiv200510502B
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Differential Geometry;
 Mathematics  Probability;
 Primary 52A22;
 52A55;
 Secondary 58B20;
 60D05;
 60F05
 EPrint:
 6 figures