May 2024 Sectional Voronoi tessellations: Characterization and high-dimensional limits
Anna Gusakova, Zakhar Kabluchko, Christoph Thäle
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Bernoulli 30(2): 1482-1501 (May 2024). DOI: 10.3150/23-BEJ1641

Abstract

The intersections of beta-Voronoi, beta-prime-Voronoi and Gaussian-Voronoi tessellations in Rd with an -dimensional affine subspaces, 1d1, are shown to be random tessellations of the same type but with different model parameters. In particular, the intersection of a classical Poisson-Voronoi tessellation with an affine subspace is shown to have the same distribution as a certain beta-Voronoi tessellation. The geometric properties of the typical cell and, more generally, typical k-faces, of the sectional Poisson-Voronoi tessellation are studied in detail. It is proved that in high dimensions, that is as d, the intersection of the d-dimensional Poison-Voronoi tessellation with an affine subspace of fixed dimension converges to the -dimensional Gaussian-Voronoi tessellation.

Funding Statement

ZK and CT were supported by the DFG priority program SPP 2265 Random Geometric Systems. AG and ZK were supported by the DFG under Germany’s Excellence Strategy EXC 2044 – 390685587, Mathematics Münster: Dynamics - Geometry - Structure.

Citation

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Anna Gusakova. Zakhar Kabluchko. Christoph Thäle. "Sectional Voronoi tessellations: Characterization and high-dimensional limits." Bernoulli 30 (2) 1482 - 1501, May 2024. https://doi.org/10.3150/23-BEJ1641

Information

Received: 1 January 2023; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699561
Digital Object Identifier: 10.3150/23-BEJ1641

Keywords: Beta-Voronoi tessellation , Gaussian-Voronoi tessellation , high-dimensional limit , Laguerre tessellation , Poisson point process , Poisson-Voronoi tessellation , sectional tessellation , Stochastic geometry , typical cell

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Vol.30 • No. 2 • May 2024
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