Random inscribed polytopes in projective geometries
- 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.
| Author: | Florian BesauGND, Daniel RosenGND, Christoph ThäleGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-100619 |
| DOI: | https://doi.org/10.1007/s00208-021-02257-9 |
| Parent Title (German): | Mathematische Annalen |
| Publisher: | Springer |
| Place of publication: | Berlin |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/08/28 |
| Date of first Publication: | 2021/08/25 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Volume: | 381 |
| First Page: | 1345 |
| Last Page: | 1372 |
| Note: | Dieser Beitrag ist auf Grund des DEAL-Springer-Vertrages frei zugänglich. |
| Dewey Decimal Classification: | Naturwissenschaften und Mathematik / Mathematik |
| open_access (DINI-Set): | open_access |
| faculties: | Fakultät für Mathematik |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
