Random permutations of countable sets

Summary The main objective of this paper is a study of random decompositions of random point configurations onR ^d into finite clusters. This is achieved by constructing for each configurationZ a random permutation ofZ with finite cycles; these cycles then form the cluster decomposition ofZ. It is argued that a good candidate for a random permutation ofZ is a Gibbs measure for a certain specification, and conditions are given for the existence and uniqueness of such a Gibbs measure. These conditions are then verified for certain random configurationsZ.