Scaling hypothesis for the Euclidean bipartite matching problem. II. Correlation functions

We analyze the random Euclidean bipartite matching problem on the hypertorus in d dimensions with quadratic cost and we derive the two-point correlation function for the optimal matching, using a proper ansatz introduced by Caracciolo [Phys. Rev. E 90, 012118 (2014)]PLEEE81539-375510.1103/PhysRevE.90.012118 to evaluate the average optimal matching cost. We consider both the grid-Poisson matching problem and the Poisson-Poisson matching problem. We also show that the correlation function is strictly related to the Green's function of the Laplace operator on the hypertorus.