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arXiv · 0903.0433

An Inverse Problem for Gibbs Fields with Hard Core Potential

L. Koralov
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Abstract

It 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.

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L. Koralov. 2009-03-03. An Inverse Problem for Gibbs Fields with Hard Core Potential. https://arxiv.org/abs/0903.0433

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