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 epsilon (Gamma)(p i sigma) of the Poisson measure pi (sigma) in terms of the extrinsic one ep silon (P)(pi sigma ,H sigmaX). More precisely, replacing pi (sigma) by a Gi bbs measure mu on the configuration space Gamma (X) we derive a relation be tween the intrinsic pre-Dirichlet form epsilon (Gamma)(mu) of the measure m u and the extrinsic epsilon (P)(mu ,H sigmaX). As a consequence we prove th e closability of epsilon (Gamma)(mu) on L-2(Gamma (X), mu) under very gener al assumptions on the interaction potential of the Gibbs measures mu.