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 et al. [Phys. Rev. E 90, 012118 (2014)] 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.