On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems

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In this paper we extend the result obtained in AKR97 (see also AKR96) on the representation of the intrinsic pre- Dirichlet form EπσΓ of the Poisson measure πσ in terms of the extrinsic one Eπσ,ₕσˣᵖ. More precisely, replacing πσ by a Gibbs measure μ on the configuration space Γₓ we derive a relation between the intrinsic pre-Dirichlet form EμΓ of the measure μ and the extrinsic one Eμ, ₕσˣᵖ. As a consequence we prove the closability of EμΓ on L²(Γₓ,μ) under very general assumptions on the interaction potential of the Gibbs measures μ.