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Revisiting Groeneveld’s approach to the virial expansion. (English) Zbl 07326367
Summary: A generalized version of Groeneveld’s convergence criterion for the virial expansion and generating functionals for weighted two-connected graphs is proven. This criterion works for inhomogeneous systems and yields bounds for the density expansions of the correlation functions $$\rho_s$$ (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 Möbius inversion on the lattice of set partitions enters the derivation of the recurrence relations.