The $β$-Delaunay tessellation: Description of the model and geometry of typical cells
Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph
Research article (journal) | Peer reviewedAbstract
In this paper we introduce two new classes of stationary random simplicial tessellations, the so-called β- and β'-Delaunay tessellations. Their construction is based on a space-time paraboloid hull process and generalizes that of the classical Poisson–Delaunay tessellation. We explicitly identify the distribution of volume-power-weighted typical cells, establishing thereby a remarkable connection to the classes of β- and β'-polytopes. These representations are used to determine the principal characteristics of such cells, including volume moments, expected angle sums, and cell intensities. 2020 Mathematics Subject Classification: Primary 60D05; 60G55; Secondary 52A22; 52B11; 53C65
Details about the publication
Journal: Advances in Applied Probability (Adv. in Appl. Probab.)
Volume: 54
Issue: 4
Page range: 1254-1290
Status: Published
Release year: 2022
Language in which the publication is written: English
DOI: 10.1017/apr.2022.6
Link to the full text: https://arxiv.org/abs/2005.13875
Keywords: Angle sums; $\beta$-Delaunay tessellation; $\beta$-polytope; $\beta'$-polytope; Laguerre tessellation;
paraboloid convexity; paraboloid hull process; Poisson point process; Poisson-Delaunay tessellation; Poisson-Voronoi tessellation; random polytope; stochastic geometry; weighted typical cell; zero cell
Authors from the University of Münster
| Gusakova, Anna | Juniorprofessorship of applied mathematics (Prof. Gusakova) |
| Kabluchko, Zakhar | Professorship for probability theory (Prof. Kabluchko) |