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

S. N. Chiu
Advances in Applied Probability
Vol. 26, No. 3 (Sep., 1994), pp. 565-576
DOI: 10.2307/1427808
Stable URL: http://www.jstor.org/stable/1427808
Page Count: 12
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Mean-Value Formulae for the Neighbourhood of the Typical Cell of a Random Tessellation
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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.

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