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arXiv · 2009.09211

Revisiting Groeneveld's approach to the virial expansion

Sabine Jansen
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Abstract

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 $\rho_s$ (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 Moebius inversion on the lattice of set partitions enters the derivation of the recurrence relations.

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Sabine Jansen. 2020-09-19. Revisiting Groeneveld's approach to the virial expansion. https://doi.org/10.1063/5.0030148

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