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Article Dans Une Revue Journal of Statistical Physics Année : 2021

Random Assignment Problems on 2d Manifolds

Résumé

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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Dates et versions

hal-02944904 , version 1 (21-09-2020)

Identifiants

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Dario Benedetto, Emanuele Caglioti, Sergio Caracciolo, Matteo d'Achille, Gabriele Sicuro, et al.. Random Assignment Problems on 2d Manifolds. Journal of Statistical Physics, 2021, 183 (34), ⟨10.1007/s10955-021-02768-4⟩. ⟨hal-02944904⟩
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