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articleNo Access
SELF-ORGANIZING BIRTH-AND-DEATH STOCHASTIC SYSTEMS IN CONTINUUM
- YURI KONDRATIEV,
- ROBERT MINLOS, and
- ELENA ZHIZHINA
Reviews in Mathematical Physics01 May 2008
Preview Abstract
We consider birth-and-death stochastic particle systems in continuum which are under a self-regulation mechanism controlling configurations of particles via a pairwise interaction between them. The latter is reflected in a potential perturbation of the free generator. We show that the ground state renormalization scheme in the considered model leads to an invariant measure, a renormalized generator and resulting equilibrium birth-and-death stochastic dynamics for the system. The proof is based on the Gibbs-type representation for related path space measure. This measure has OS-positivity property and is constructed via the cluster expansion method.

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