For a class of translation-invariant pair potentials ϕ in \((\mathbb{R}^{d},z\lambda )\) satisfying a stability and regularity condition, we choose z so small that the associated collection \(\mathcal{ G}(\phi,z\lambda )\) of Gibbs processes contains at least the stationary process G, which is a Gibbs process in the sense of DLR and is given by the limiting Gibbs process with empty boundary conditions. Using an abstract version of the method of cluster expansions and Dobrushin’s approach to the central limit theorem, we present a central limit theorem for the particle numbers of G.

中文翻译：

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经典气体的中心极限定理

对于\((\mathbb{R}^{d},z\lambda )\)中的一类平移不变对势ψ满足稳定性和规律性条件，我们选择z如此小，使得相关集合\(\mathcal吉布斯过程的{ G}(\phi,z\lambda )\)至少包含平稳过程 G，它是 DLR 意义上的吉布斯过程，由具有空边界条件的极限吉布斯过程给出。使用簇展开方法的抽象版本和 Dobrushin 的中心极限定理方法，我们提出了 G 的粒子数的中心极限定理。