On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems
da Silva, José
da Silva
José
Kondratiev, Yuri
Kondratiev
Yuri
Röckner, Michael
Röckner
Michael
In this paper we extend the result obtained in [AKR98] (see also [AKR96a]) on the representation of the intrinsic pre-Dirichlet form epsilon (Gamma)(pi sigma) of the Poisson measure pi (sigma) in terms of the extrinsic one epsilon (P)(pi sigma ,H sigmaX). More precisely, replacing pi (sigma) by a Gibbs measure mu on the configuration space Gamma (X) we derive a relation between the intrinsic pre-Dirichlet form epsilon (Gamma)(mu) of the measure mu and the extrinsic epsilon (P)(mu ,H sigmaX). As a consequence we prove the closability of epsilon (Gamma)(mu) on L-2(Gamma (X), mu) under very general assumptions on the interaction potential of the Gibbs measures mu.
222
141-157
141-157
WILEY-V C H VERLAG GMBH
2001