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. 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.

References in corpus (3)

• Scaling hypothesis for the Euclidean bipartite matching problem
• On the one dimensional Euclidean matching problem: exact solutions, correlation functions and universality
• Correlation function for the Grid-Poisson Euclidean matching on a line and on a circle

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