Revisiting Groeneveld's approach to the virial expansion

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.

arXiv comment25 pages

References in corpus (14)

• Perfect simulation for interacting point processes, loss networks and Ising models
• Abstract cluster expansion with applications to statistical mechanical systems
• Cluster expansion in the canonical ensemble
• On the convergence of cluster expansions for polymer gases
• Cluster expansions for Gibbs point processes
• Mayer and virial series at low temperature
• Cluster and virial expansions for the multi-species Tonks gas
• Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics
• Finite volume corrections and decay of correlations in the canonical ensemble
• Correlation of clusters: Partially truncated correlation functions and their decay
• Virial Expansion Bounds Through Tree Partition Schemes
• Stability of gas measures under perturbations and discretizations
• Thermodynamics of a hierarchical mixture of cubes
• A Solution to the Combinatorial Puzzle of Mayer's Virial Expansion