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 [Phys. Rev. E 90, 012118 (2014)]PLEEE81539-375510.1103/PhysRevE.90.012118 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.
Scaling hypothesis for the Euclidean bipartite matching problem. II. Correlation functions / S. Caracciolo, G. Sicuro. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 91:6(2015), pp. 062125.1-062125.8. [10.1103/PhysRevE.91.062125]
Scaling hypothesis for the Euclidean bipartite matching problem. II. Correlation functions
S. CaraccioloPrimo
;
2015
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 [Phys. Rev. E 90, 012118 (2014)]PLEEE81539-375510.1103/PhysRevE.90.012118 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.
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