title: Quadratic Stochastic Euclidean Bipartite Matching Problem.
abstract: We propose a new approach for the study of the quadratic stochastic Euclidean bipartite matching problem between two sets of N points each, N≫1. The points are supposed independently randomly generated on a domain Ω⊂R^{d} with a given distribution ρ(x) on Ω. 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 a particular case.
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, Rio de Janeiro, Brazil.
authors.forename: Gabriele
authors.initials: G
authors.lastname: Sicuro