相互作用粒子系统的内禀Dirichlet型与外禀Dirichlet型之间的关系
On a relation between intrinsic and extrinsic Dirichlet forms for interacting particle systems
摘要：
本文推广了在\cite{AKR97}（也见\cite {AKR 96}）中得到的关于泊松测度$π_σ$的内在预狄利克雷形式$\mathcal{E}_{π_σ}^Γ$用外在形式$\mathcal{E}_{π_σ,H_σ^{X}}^{P}$表示的结果.更准确地说，在位形空间$Γ_{X}$上用吉布斯测度$μ$代替$π_σ$，我们导出了测度$μ$的内在预狄利克雷形式$\mathcal{E}_μ^Γ$与外在形式$\mathcal{E}_{μ, H_σ^{X}}^{P}$之间的关系。因此，我们证明了封闭性的$\mathcal{E}_μ^Γ$上$L^{2}(Γ_{X},μ)$的吉布斯措施$μ$的相互作用潜力的非常一般的假设。
英文摘要：
In 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 $μ$.
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