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Random Assignment Problems on 2d Manifolds

Abstract : We consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold Ω of unit area. It is known that the average cost scales as E[Ω (N)] ∼ 1/2π ln N with a correction that is at most of order √ ln N ln ln N. In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first Ω-dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace-Beltrami operator on Ω. We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.
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https://hal.archives-ouvertes.fr/hal-02944904
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Submitted on : Monday, September 21, 2020 - 6:15:06 PM
Last modification on : Friday, July 2, 2021 - 10:02:05 AM
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Dario Benedetto, Emanuele Caglioti, Sergio Caracciolo, Matteo d'Achille, Gabriele Sicuro, et al.. Random Assignment Problems on 2d Manifolds. In press. ⟨hal-02944904⟩

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