Random inscribed polytopes in projective geometries
| Autor: | Florian Besau, Christoph Thäle, Daniel Rosen |
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| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Convex hull Surface (mathematics) Euclidean space General Mathematics Probability (math.PR) Boundary (topology) Metric Geometry (math.MG) Polytope Primary 52A22 52A55 Secondary 58B20 60D05 60F05 Combinatorics Mathematics - Metric Geometry Differential Geometry (math.DG) FOS: Mathematics Mathematics::Metric Geometry Convex body Random variable Mathematics - Probability Central limit theorem Mathematics |
| Zdroj: | Mathematische Annalen. 381:1345-1372 |
| ISSN: | 1432-1807 0025-5831 |
| DOI: | 10.1007/s00208-021-02257-9 |
| Popis: | 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 Berry-Esseen bounds for functionals of independent random variables. Comment: 6 figures |
| Databáze: | OpenAIRE |
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