Bogachev, L and Daletskii, A (2012) Gibbs cluster measures on configuration spaces. Journal of Functional Analysis. ISSN 0022-1236 (In Press)
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Abstract
The distribution gcl of a Gibbs cluster point process in X = R^d (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 ˆg in the space of configurations Γ_X={(x,y)}}, where x indicates a cluster "center" and y represents a corresponding cluster relative to x. We show that the measure g_cl is quasi-invariant with respect to the group Diff0(X) of compactly supported diffeomorphisms of X, and prove an integration-by-parts formula for g_cl. The associated equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms. These results are quite general; in particular, the uniqueness of the background Gibbs measure g is not required. The paper is an extension of the earlier results for Poisson cluster measures [J. Funct. Analysis 256 (2009) 432–478], where a different projection construction was utilized specific to this "exactly soluble" case.
| Item Type: | Article |
|---|---|
| Copyright, Publisher and Additional Information: | © 2011 Elsevier. This is an author produced version of a paper subsequently published in Journal of Functional Analysis . Uploaded in accordance with the publisher's self-archiving policy. |
| Keywords: | Cluster point process, Gibbs measure, Poisson measure, Interaction potential, Configuration space, Quasi-invariance, Integration by parts, Dirichlet form, Stochastic dynamics |
| Academic Units: | The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) The University of York > Mathematics (York) |
| Depositing User: | Symplectic Publications |
| Date Deposited: | 17 Oct 2011 14:25 |
| Last Modified: | 08 Feb 2013 17:34 |
| Status: | In Press |
| Publisher: | Elsevier |
| URI: | http://eprints.whiterose.ac.uk/id/eprint/43331 |
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