Analysis on configuration spaces and Gibbs cluster ensembles |
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| Authors: | L Bogachev A Daletskii |
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| Institution: | (1) Department of Statistics, University of Leeds, Leeds, LS2 9JT, UK;(2) Department of Mathematics, University of York, York, YO10 5DD, UK |
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| 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.
Dedicated to the memory of Vladimir Geyler
Research supported in part by DFG Grant 436 RUS 113/722. |
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