Scaling hypothesis for the Euclidean bipartite matching problem

02/27/2014

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by   Sergio Caracciolo, et al.

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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 non-trivial 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.