Advances in Applied Probability

Some distributional results for Poisson-Voronoi tessellations

Volker Baumstark and Günter Last

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Abstract

We consider the Voronoi tessellation based on a stationary Poisson process N in ℝd. We provide a complete and explicit description of the Palm distribution describing N as seen from a randomly chosen (typical) point on a k-face of the tessellation. In particular, we compute the joint distribution of the d-k+1 neighbours of the k-face containing the typical point. Using this result as well as a fundamental general relationship between Palm probabilities, we then derive some properties of the typical k-face and its neighbours. Generalizing recent results of Muche (2005), we finally provide the joint distribution of the typical edge (typical 1-face) and its neighbours.

Article information

Source
Adv. in Appl. Probab. Volume 39, Number 1 (2007), 16-40.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.aap/1175266467

Digital Object Identifier
doi:10.1239/aap/1175266467

Mathematical Reviews number (MathSciNet)
MR2307869

Zentralblatt MATH identifier
1119.60004

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60G55: Point processes

Keywords
Voronoi tessellation Poisson process random measure Palm distribution typical face typical edge

Citation

Baumstark, Volker; Last, Günter. Some distributional results for Poisson-Voronoi tessellations. Adv. in Appl. Probab. 39 (2007), no. 1, 16--40. doi:10.1239/aap/1175266467. https://projecteuclid.org/euclid.aap/1175266467


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