论文标题
重新访问Groeneveld的病毒扩展方法
Revisiting Groeneveld's approach to the virial expansion
论文作者
论文摘要
证明了Groeneveld的融合标准，用于病毒扩展和生成加权$ 2 $连接的图形的功能。该标准适用于不均匀的系统，并产生相关函数的密度扩展的界限$ρ_s$（又称分布函数或阶乘力矩度量），用于与成对相互作用的大型跨型吉布斯度量。该证明基于与Kirkwood-Salsburg积分方程相关函数相关的图形权重的复发关系。该证明不使用密度 - 活性扩展的反转，但是在设定分区的晶格上的Moebius反转进入了复发关系的推导。
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.
