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 / S. Caracciolo, M.P. D'Achille, E.M. Malatesta, G. Sicuro. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 95:5-1(2017 May), pp. 052129.1-052129.15.
Finite-size corrections in the random assignment problem
S. CaraccioloPrimo
;E.M. MalatestaPenultimo
;
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.File | Dimensione | Formato | |
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