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An Inverse Problem for Gibbs Fields with Hard Core Potential | | L. Koralov
; | | Date: |
3 Mar 2009 | | 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 $overline{
ho}_1$ and a sufficiently small
function $overline{
ho}_2(x)$, $x in mathbb{R}^d$, 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 $overline{
ho}_1$ is the density and
$overline{
ho}_2$ is the pair correlation function of the corresponding Gibbs
field. | | Source: | arXiv, 0903.0433 | | Services: | Forum | Review | PDF | Favorites | |
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