Cluster point processes on manifolds (Q1931524)

This paper is devoted to the study of the probability distribution of a general cluster point in a Riemannian manifold (with independent random clusters attached to points of a configuration with a given distribution) via the projection of an auxiliary measure in an adequate space of configurations. The authors show that this measure is quasi invariant with respect to the group of compactly supportted diffeomorphisms of the manifold, and prove an integration-by-parts formula for this measure. The associated equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms. General constructions are illustrated by examples including Euclidean spaces, Lie groups, homogeneous spaces, Riemannian manifolds of non-positive curvature and metric spaces.