Equilibrium stochastic dynamics of Poisson cluster ensembles

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Publication details

JournalCondensed matter physics
DatePublished - 2008
Issue number2
Volume11
Number of pages13
Pages (from-to)261-273
Original languageEnglish

Abstract

The distribution mu of a Poisson cluster process in chi = R-d (with n-point clusters) is studied via the projection of an auxiliary Poisson measure in the space of configurations in chi(n), with the intensity measure being the convolution of the background intensity (of cluster centres) with the probability distribution of a generic cluster. We show that mu is quasi-invariant with respect to the group of compactly supported diffeomorphisms of chi, and prove an integration by parts formula for mu. The corresponding equilibrium. stochastic dynamics is then constructed using the method of Dirichlet forms.

    Research areas

  • cluster point process, Poisson measure, configuration space, quasi-invariance, integration by parts, Dirichlet form, stochastic dynamics, CONFIGURATION-SPACES, GEOMETRY

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