Quadratic stochastic Euclidean bipartite matching problem

We propose a new approach for the study of the quadratic stochastic Euclidean bipartite matching problem between two sets of $N$ points each, $N\gg 1$. The points are supposed independently randomly generated on a domain $Ω\subset\mathbb R^d$ with a given distribution $ρ(\mathbf x)$ on $Ω$. In particular, we derive a general expression for the correlation function and for the average optimal cost of the optimal matching. A previous ansatz for the matching problem on the flat hypertorus is obtained as particular case.

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