Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591000 | Journal of Functional Analysis | 2013 | 43 Pages |
Abstract
The probability distribution gcl of a Gibbs cluster point process in X=Rd (with i.i.d. random clusters attached to points of a Gibbs configuration with distribution g) is studied via the projection of an auxiliary Gibbs measure in the space of configurations , where x∈X indicates a cluster “center” and represents a corresponding cluster relative to x. We show that the measure gcl is quasi-invariant with respect to the group Diff0(X) of compactly supported diffeomorphisms of X, and prove an integration-by-parts formula for gcl. The associated equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms.
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