再论Groeneveld的维里展开法
Revisiting Groeneveld's approach to the virial expansion
摘要：
证明了加权$2$ -连通图的维里展开和生成泛函的Groeneveld收敛准则的一个推广形式。该准则适用于非齐次系统，并给出了关联函数$ρ_s$（a.k.a.分布函数或阶乘矩测量）的巨正则吉布斯措施与成对的相互作用。证明是基于递归关系的图的权重相关的柯克伍德-萨尔斯堡积分方程的关联函数。证明不使用反演的密度活动的扩展，但莫比乌斯反演格集分区进入推导的递归关系。
英文摘要：
A generalized version of Groeneveld's convergence criterion for the virial expansion and generating functionals for weighted $2$-connected graphs is proven. The criterion works for inhomogeneous systems and yields bounds for the density expansions of the correlation functions $ρ_s$ (a.k.a. distribution functions or factorial moment measures) of grand-canonical Gibbs measures with pairwise interactions. The proof is based on recurrence relations for graph weights related to the Kirkwood-Salsburg integral equation for correlation functions. The proof does not use an inversion of the density-activity expansion, however a Moebius inversion on the lattice of set partitions enters the derivation of the recurrence relations.
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