Abstract
The distribution µ of a Gibbs cluster point process in χ = ℝd (with n-point clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in χ × χ n. We show that µ is quasi-invariant with respect to the group Diff0(χ) of compactly supported diffeomorphisms of χ and prove an integration-by-parts formula for µ. The corresponding equilibrium stochastic dynamics is then constructed by using the method of Dirichlet forms.
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