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arXiv · 1702.05991

Finite-size corrections in the random assignment problem

Sergio Caracciolo·Matteo P. D'Achille·Enrico M. Malatesta·Gabriele Sicuro
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Abstract

We analytically derive, in the context of the replica formalism, the first finite size corrections to the average optimal cost in the random assignment problem for a quite generic distribution law for the costs. We show that, when moving from a power-law distribution to a $Γ$ distribution, the leading correction changes both in sign and in its scaling properties. We also examine the behavior of the corrections when approaching a $δ$-function distribution. By using a numerical solution of the saddle-point equations, we provide predictions that are confirmed by numerical simulations.

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Sergio Caracciolo, Matteo P. D'Achille, Enrico M. Malatesta, Gabriele Sicuro. 2017-05-17. Finite-size corrections in the random assignment problem. https://doi.org/10.1103/physreve.95.052129

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