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.
Original languageEnglish
Pages (from-to)565-576
Number of pages12
JournalAdvances in Applied Probability
Volume26
Issue number3
DOIs
Publication statusPublished - Sep 1994
Externally publishedYes

User-Defined Keywords

  • Aboav's Law
  • Lewis's Law
  • Mean-Value Formulae
  • Mosaics
  • Neighbourhood
  • Palm Distribution
  • Random Tessellations
  • Statistical Crystallography
  • Stochastic Geometry

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