Random mosaics with cells of general topology

Extract

This paper considers a structure, named a ‘random partition process’, which is a generalisation of a random tessellation. The cells, possibly multi-part and with holes, have a general topology summarised by the Euler characteristic. Vertices of all orders are allowed. Using the tools of ergodic theory, all of the formulae, from the traditional theory of random tessellations with convex cells, are generalised. Some motivating examples are given.