  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. 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.
