Some distributional results for Poisson-Voronoi tessellations
Volker Baumstark and Günter Last
Source: Adv. in Appl. Probab.
Volume 39, Number 1
(2007), 16-40.
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.
Primary Subjects: 60D05, 60G55
Keywords: Voronoi tessellation; Poisson process; random measure; Palm distribution; typical face; typical edge
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1175266467
Digital Object Identifier: doi:10.1239/aap/1175266467
Zentralblatt MATH identifier:
1119.60004
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