Bogachev, L and Daletskii, A (2013) Cluster point processes on manifolds. Journal of Geometry and Physics, 63 (1). 45 - 79 (35). ISSN 1435-9855
Abstract
The probability distribution μ_cl of a general cluster point process in a Riemannian manifold X (with independent random clusters attached to points of a configuration with distribution μ) is studied via the projection of an auxiliary measure ˆμ in the space of configurations ˆ Γ = {(x,y)} ⊂ X × X, where x ∈ X indicates a cluster "centre" and y ∈ X represents a corresponding cluster relative to x. We show that the measure μ_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 μcl. The associated equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms. General constructions are illustrated by examples including Euclidean spaces, Lie groups, homogeneous spaces, Riemannian manifolds of non-positive curvature and metric spaces.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2013. Elsevier. Uploaded in accordance with the publisher's self-archiving policy. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Geometry and Physics . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Geometry and Physics,63,(2013) DOI10.1016/j.geomphys.2012.09.007 |
Keywords: | Cluster point process, Configuration space, Riemannian manifold, Quasi-invariance, Integration by parts, Stochastic dynamics |
Dates: |
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Institution: | The University of Leeds, The University of York |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Mar 2013 10:45 |
Last Modified: | 29 Oct 2017 16:09 |
Published Version: | http://dx.doi.org/10.1016/j.geomphys.2012.09.007 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.geomphys.2012.09.007 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:74924 |