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, $Ngg 1$. The points are supposed independently randomly generated on a domain $Omegasubsetmathbb R^d$ with a given distribution $ ho(mathbf x)$ on $Omega$. 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.