We study the convergence of cluster and virial expansions for systems of particles subject to positive two-body interactions. Our results strengthen and generalize existing lower bounds on the radii of convergence and on the value of the pressure. Our treatment of the cluster coefficients is based on expressing the truncated weights in terms of trees and partition schemes, and generalize to soft repulsions previous approaches for models with hard exclusions. Our main theorem holds in a very general framework that does not require translation invariance and is applicable to models in general measure spaces. Our virial results, stated only for homogeneous single-space systems, rely on an approach due to Ramawadh and Tate. The virial coefficients are computed using Lagrange inversion techniques but only at the level of formal power series, thereby yielding diagrammatic expressions in terms of trees, rather than the doubly connected diagrams traditionally used. We obtain a new criterion that strengthens, for repulsive interactions, the best criterion previously available (proposed by Groeneveld and proven by Ramawadh and Tate). We illustrate our results with a few applications showing noticeable improvements in the lower bound of convergence radii.

中文翻译：

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排斥经典气体的簇和维力膨胀的收敛

我们研究了受正二体相互作用影响的粒子系统的簇和维里膨胀的收敛性。我们的结果加强并概括了收敛半径和压力值的现有下界。我们对聚类系数的处理基于根据树和分区方案表达截断的权重，并将之前的硬排除模型推广到软排斥。我们的主要定理在一个非常通用的框架中成立，该框架不需要平移不变性，并且适用于一般度量空间中的模型。我们的维里结果，仅针对同构单空间系统，依赖于 Ramawadh 和​​ Tate 的方法。维里系数是使用拉格朗日反演技术计算的，但仅限于形式幂级数，从而以树的形式产生图解表达，而不是传统上使用的双连通图。我们获得了一个新标准，该标准加强了之前可用的最佳标准（由 Groeneveld 提出并由 Ramawadh 和​​ Tate 证明），用于排斥相互作用。我们通过一些应用来说明我们的结果，这些应用显示收敛半径下限的显着改进。