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Gibbs cluster measures on configuration spaces

TitleGibbs cluster measures on configuration spaces
Publication TypeJournal Article
Year of Publication2013
AuthorsBogachev L, Daletskii A
Refereed DesignationRefereed
JournalJournal of Functional Analysis
Start Page508
Date Published01/2013
AbstractThe probability distribution $g_{cl}$ of a Gibbs cluster point process in a Euclidean space $X$(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 in the space of configurations in $X\times X^\infty$. We show that 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 gcl. 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.

Edited 22 Jan 2013 - 11:15 by cac7

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