Equilibrium stochastic dynamics of Poisson cluster ensembles

TY - JOUR

T1 - Equilibrium stochastic dynamics of Poisson cluster ensembles

AU - Bogachev, L.

AU - Daletskii, A.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - cluster point process

KW - Poisson measure

KW - configuration space

KW - quasi-invariance

KW - integration by parts

KW - Dirichlet form

KW - stochastic dynamics

KW - CONFIGURATION-SPACES

KW - GEOMETRY

UR - http://www.scopus.com/inward/record.url?scp=37349109014&partnerID=8YFLogxK

M3 - Article

SN - 1607-324X

VL - 11

SP - 261

EP - 273

JO - Condensed matter physics

JF - Condensed matter physics

IS - 2

ER -