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# Leonid Koralov : An Inverse Problem for Gibbs Fields

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 $\mathbb{Z}^d$ or $\mathbb{R}^d$). We consider a converse problem. Namely, we show that for a sufficiently small constant $\overline{\rho}_1$ and a sufficiently small function $\overline{\rho}_2(x)$, $x \in \mathbb{Z}^d$ or $\mathbb{R}^d$, there exist a hard core pair potential, and a value of activity, such that $\overline{\rho}_1$ is the density and $\overline{\rho}_2$ is the pair correlation function of the corresponding Gibbs field.

**Category**: Probability**Duration**: 01:34:43**Date**: September 27, 2007 at 4:25 PM**Views**: 168-
**Tags:**seminar, Probability Seminar

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