Details

Autor(en) / Beteiligte

• Besau, Florian
• Rosen, Daniel
• Thäle, Christoph

Titel

Random inscribed polytopes in projective geometries

Ist Teil von

• Mathematische annalen, 2021-12, Vol.381 (3-4), p.1345-1372

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2021

Link zum Volltext

Quelle

SpringerNature Journals

Beschreibungen/Notizen

• 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 a Berry–Esseen bound for functionals of independent random variables.