Construction and Uniqueness of Classical Gases

S. Poghosyan, H. Zessin

2026, v.32, Issue 1, 149-160

ABSTRACT

For a pair potential Φ in Euclidean space ℝ^d satisfying some natural and sufficiently general conditions in the sense of Penrose [1] and Poghosyan and Ueltschi [2] we define by means of the so-called Ursell kernel a function r which is shown to be the correlation function of a unique process G, the limiting Gibbs process for (Φ, ρ) with empty boundary conditions. This process is exhibited as a Gibbs process in the sense of Dobrushin, Lanford and Ruelle for a class of pair potentials, which contains classical stable and hard-core potentials that are called Penrose potentials here. Particularly, a class of positive potentials is included. Finally, for some class of Penrose potentials we show that G is the unique Gibbs process for Φ. We use the classical method of Kirkwood-Salsburg equations. A decisive role is played by a generalization of Ruelle’s estimate for correlation functions.

doi:10.61102/1024-2953-mprf.2026.32.1.007

Keywords: Limiting Gibbs process, Kirkwood-Salsburg equations, Ruelle estimate, Uniqueness

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