Random Mosaics

Mosaics arise frequently as models in materials science, biology, geology, telecommunications, and in data and point pattern analysis. Very often the data from which a mosaic is constructed is random, hence we arrive at a random mosaic. Such a random mosaic can be considered as a special particle process or as a random closed set having a special structure. Random mosaics provide a convenient and important model for illustrating some of the general concepts discussed in previous parts of these lecture notes. In particular, the investigation of random mosaics naturally requires a combination of probabilistic, geometric and combinatorial ideas. In this brief survey of selected results and methods related to random mosaics, we will mainly concentrate on classical topics which are contained in the monographs [9], [12] and [14]. A survey with a different emphasis is provided in [10]. Some of the more recent developments related to modelling of communication networks, iterated constructions of random mosaics and related central limit theorems cannot be discussed here. But there is also interesting recent research which is concerned with obtaining quantitative information about various shape characteristics of random mosaics. In the final part of this appendix, we will report on work carried out in this direction.