Concentration of the cost of a random matching problem

Let Mn be the minimum cost of a perfect matching on a complete graph on n vertices whose edges are assigned independent exponential costs. It follows from work of D. Aldous that Mn converges in probabil- ity to …2=12. This was earlier conjectured by M. Mezard and G. Parisi. We establish the more precise result that E fl flMn ¡ …2=12 fl fl = O(n¡1=2).