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Gibbs cluster measures on configuration spaces

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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