Finite-size corrections in the random assignment problem

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 Gamma distribution, the leading correction changes both in sign and in its scaling properties. We also examine the behavior of the corrections when approaching a delta-function distribution. By using a numerical solution of the saddle-point equations, we provide predictions that are confirmed by numerical simulations.