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

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dc.creatorKondratiev, Yuri
dc.creatorSilva, Jose Luis
dc.creatorRoeckner, Michael
dc.date1999-08-12
dc.date.accessioned2026-07-07T05:30:17Z
dc.date.available2026-07-07T05:30:17Z
dc.descriptionIn this paper we extend the result obtained in \cite{AKR97} (see also \cite {AKR96}) on the representation of the intrinsic pre- Dirichlet form $\mathcal{E}_{π_σ}^Γ$ of the Poisson measure $π_σ$ in terms of the extrinsic one $\mathcal{E}_{π_σ,H_σ^{X}}^{P}$. More precisely, replacing $π_σ$ by a Gibbs measure $μ$ on the configuration space $Γ_{X}$ we derive a relation between the intrinsic pre-Dirichlet form $\mathcal{E}_μ^Γ$ of the measure $μ$ and the extrinsic one $\mathcal{E}_{μ, H_σ^{X}}^{P}$. As a consequence we prove the closability of $\mathcal{E}_μ^Γ$ on $L^{2}(Γ_{X},μ)$ under very general assumptions on the interaction potential of the Gibbs measures $μ$.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/9908055
dc.identifierhttp://arxiv.org/abs/math/9908055
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78941
dc.subjectFunctional Analysis
dc.titleOn a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems
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