MEAN-VALUE FORMULAS FOR THE NEIGHBORHOOD OF THE TYPICAL CELL OF A RANDOM TESSELLATION

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-ca lled Aboav's law. This law now plays a central role in River'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.