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.

Finite-size corrections in the random assignment problem

Enrico M. , Malatesta;
2017

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.
2017
2017
Caracciolo, Sergio; D'Achille, Matteo P.; Malatesta, ENRICO MARIA; Sicuro, Gabriele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4029518
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