On a Relation between Intrinsic and Extrinsic Dirichlet Forms for Interacting Particle Systems

In this paper we extend the result obtained in AKR98] (see also AKR96a]) on the representation of the intrinsic pre–Dirichlet form ℰ^Γ of the Poisson measure π_σ in terms of the extrinsic one ℰ^P. More precisely, replacing π_σ by a Gibbs measure μ on the configuration space Γ_X we derive a relation between the intrinsic prend–Dirichlet form ℰ^Γ_μ of the measure μ and the extrinsic one ℰ^P. As a consequence we prove the closability of ℰ^Γ_μ on L²(Γ_X, μ) under very general assumptions on the interaction potential of the Gibbs measures μ.