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Gibbs cluster measures on configuration spaces

Bogachev, L and Daletskii, A (2013) Gibbs cluster measures on configuration spaces. Journal of Functional Analysis, 264 (2). 508 - 550 (43). ISSN 0022-1236


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The probability distribution g_cl 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 ĝ in the space of configurations ^γ={(x,\bar{y})}, where x∈X indicates a cluster "center" and y∈\mathfrak{X}=\sqcup_{n} X^n represents a corresponding cluster relative to x. We show that the measure g_cl 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 g_cl. The associated equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms.

Item Type: Article
Copyright, Publisher and Additional Information: © 2012, 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; Configuration space; Gibbs measure; Poisson measure; Quasi-invariance; Integration by parts; Dirichlet form; Stochastic dynamics
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds)
The University of York > Mathematics (York)
Depositing User: Symplectic Publications
Date Deposited: 17 Oct 2011 14:25
Last Modified: 12 Nov 2015 10:59
Published Version: http://dx.doi.org/10.1016/j.jfa.2012.11.002
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.jfa.2012.11.002
URI: http://eprints.whiterose.ac.uk/id/eprint/43331

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