Random permutations of countable sets (Q756299)

The main objective of this paper is a study of random decompositions of random point configurations on \(\mathbb R^ d\) into finite clusters. This is achieved by constructing for each configuration \(Z\) a random permutation of \(Z\) with finite cycles; these cycles then form the cluster decomposition of \(Z\). It is argued that a good candidate for a random permutation of \(Z\) 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 configurations \(Z\).