title: Scaling hypothesis for the Euclidean bipartite matching problem.
abstract: We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic prediction of the large N limit of the average cost in dimension d = 1,2 and of the subleading correction in higher dimension. A nontrivial scaling exponent, γ(d) = d-2/d, which differs from the monopartite's one, is found for the subleading correction. We argue that the same scaling holds true for a generic cost exponent in dimension d > 2.
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Milano and INFN, via Celoria, I-20133 Milano, Italy.
authors.forename: S
authors.initials: S
authors.lastname: Caracciolo
authors.affiliation: Dipartimento di Fisica, Università "La Sapienza," P.le A. Moro 2, I-00185 Rome, Italy.
authors.forename: C
authors.initials: C
authors.lastname: Lucibello
authors.affiliation: Dipartimento di Fisica, INFN-Sezione di Roma 1, CNR-IPCF UOS Roma Kerberos, Università "La Sapienza," P.le A. Moro 2, I-00185 Rome, Italy.
authors.forename: G
authors.initials: G
authors.lastname: Parisi
authors.affiliation: Dipartimento di Fisica "Enrico Fermi," Università di Pisa, and INFN-Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy.
authors.forename: G
authors.initials: G
authors.lastname: Sicuro
mesh_terms: D016012:Poisson Distribution; D013223:Statistics as Topic / Q000379:methods*