Gibbs measures over permutations of point processes with low density

Inés Armendáriz, Pablo A. Ferrari, Nicolás Frevenza

We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp \{-\alpha {\sum }_{x}V(\sigma (x)-x)\},$ whe…