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 dual and the mean width polyhedral sets are obtained. deduce these results by proving a general theorem weighted volume convex hull points chosen from boundary smooth body according to positive continuous density Euclidean space. background geometric estimates surface bodies Berry–Esseen bound functionals independent variables.