A central limit theorem for a classical gas

Abstract

For a class of translation-invariant pair potentials ϕ in (mathbb{R}^{d},zlambda ) satisfying a stability and regularity condition, we choose z so small that the associated collection mathcal{ G}(phi,zlambda ) of Gibbs processes contains at least the stationary process G, which is a Gibbs process in the sense of DLR and is given by the limiting Gibbs process with empty boundary conditions. Using an abstract version of the method of cluster expansions and Dobrushin’s approach to the central limit theorem, we present a central limit theorem for the particle numbers of G.