Analysis on configuration spaces and Gibbs cluster ensembles

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JournalRussian journal of mathematical physics
DatePublished - Dec 2007
Issue number4
Number of pages12
Pages (from-to)397-408
Original languageEnglish


The distribution mu of a Gibbs cluster point process in X = R-d ( with n-point clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in X x X-n. We show that mu is quasi-invariant with respect to the group Diff(0)(X) of compactly supported diffeomorphisms of X and prove an integration-by-parts formula for mu. The corresponding equilibrium stochastic dynamics is then constructed by using the method of Dirichlet forms.

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