Analyticity for Classical Gasses via Recursion

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We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the bound for analyticity is by a factor $$e^2$$ over the classical cluster expansion approach and a factor e over the known limit of cluster expansion convergence. The criterion is based on a contractive property of a recursive computation of the density of a point process. The key ingredients in our proofs include an integral identity for the density of a Gibbs point process and an adaptation of the algorithmic correlation decay method from theoretical computer science. We also deduce from our results an improved bound for analyticity of the pressure as a function of the density.