Gusakova, Anna; Kabluchko, Zakhar; Thäle, Christoph
Research article (journal) | Peer reviewedThe β-Delaunay tessellation in Rd-1 is a generalization of the classical Poisson-Delaunay tessellation. As a first result of this paper we show that the shape of a weighted typical cell of a β-Delaunay tessellation, conditioned on having large volume, is close to the shape of a regular simplex in Rd-1. This generalizes earlier results of Hug and Schneider about the typical (non-weighted) Poisson-Delaunay simplex. Second, the asymptotic behaviour of the volume of weighted typical cells in high-dimensional β-Delaunay tessellation is analysed, as d → ∞. In particular, various high dimensional limit theorems, such as quantitative central limit theorems as well as moderate and large deviation principles, are derived. 2010 Mathematics Subject Classification. 52A22, 52A40, 60D05, 60F05, 60F10.
Gusakova, Anna | Juniorprofessorship of applied mathematics (Prof. Gusakova) |
Kabluchko, Zakhar | Professorship for probability theory (Prof. Kabluchko) |