title: Scaling hypothesis for the Euclidean bipartite matching problem. II. Correlation functions.
abstract: 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.
authors.affiliation: Dipartimento di Fisica, University of Milan and INFN, via Celoria 16, I-20133 Milan, Italy.
authors.forename: Sergio
authors.initials: S
authors.lastname: Caracciolo
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.
authors.forename: Gabriele
authors.initials: G
authors.lastname: Sicuro