2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222102It is well known that for a regular stable potential of pair interaction and a small value of activity one can define the corresponding Gibbs field (a measure on the space of configurations of points in $\mathbb{R}^d$). In this paper we consider a converse problem. Namely, we show that for a sufficiently small constant $\overlineρ_1$ and a sufficiently small function $\overlineρ_2(x)$, $x \in \mathbb{R}^d$, that is equal to zero in a neighborhood of the origin, there exist a hard core pair potential, and a value of activity, such that $\overlineρ_1$ is the density and $\overlineρ_2$ is the pair correlation function of the corresponding Gibbs field.Mathematical PhysicsProbability60G55, 60G60text