The typical cell of a Voronoi tessellation on the sphere
- The typical cell of a Voronoi tessellation generated by \(\it n\) + 1 uniformly distributed random points on the \(\it d\)-dimensional unit sphere \(\mathbb{S}^{d}\) is studied. Its \(\it f\)-vector is identified in distribution with the f-vector of a beta' polytope generated by n random points in \(\mathbb{R}^{d}\). Explicit formulas for the expected \(\it f\)-vector are provided for any \(\it d\) and the low-dimensional cases \(\it d\)\(\in\){2,3,4} are studied separately. This implies an explicit formula for the total number of \(\it k\)-dimensional faces in the spherical Voronoi tessellation as well.
| Author: | Zakhar KabluchkoGND, Christoph ThäleGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-98812 |
| DOI: | https://doi.org/10.1007/s00454-021-00315-2 |
| Parent Title (English): | Discrete & computational geometry |
| Publisher: | Springer |
| Place of publication: | New York |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2023/05/10 |
| Date of first Publication: | 2021/07/04 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | Beta polytope; Beta' polytope; Spherical stochastic geometry; Typical cell; Voronoi tessellation |
| Volume: | 66 |
| First Page: | 1330 |
| Last Page: | 1350 |
| 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 |
