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Mean-Value Formulae for the Neighbourhood of the Typical Cell of a Random Tessellation

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

S. N. Chiu
S. N. Chiu*
Affiliation:
Freiberg University of Mining and Technology
*
* Postal address: TU Bergakademie Freiberg, Institut für Stochastik, D-09596 Freiberg, Germany. Supported by a DAAD scholarship. DAAD, Postfach 200 404, D-53134 Bonn, Germany.
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Abstract

The mean number of edges of a randomly chosen neighbouring cell of the typical cell in a planar stationary tessellation, under the condition that it has n edges, has been studied by physicists for more than 20 years. Experiments and simulation studies led empirically to the so-called Aboav's law. This law now plays a central role in Rivier's (1993) maximum entropy theory of statistical crystallography. Using Mecke's (1980) Palm method, an exact form of Aboav's law is derived. Results in higher-dimensional cases are also discussed.

Keywords

ABOAV'S LAWLEWIS'S LAWMEAN-VALUE FORMULAEMOSAICSNEIGHBOURHOODPALM DISTRIBUTIONRANDOM TESSELLATIONSSTATISTICAL CRYSTALLOGRAPHYSTOCHASTIC GEOMETRY

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994 , pp. 565 - 576
Copyright
Copyright © Applied Probability Trust 1994 

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