Concentration of the cost of a random matching problem

Abstract

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 probability to π2/12. This was earlier conjectured by M. Mézard and G. Parisi. We establish the more precise result that E ∣Mn − π2/12 ∣∣ = O(n−1/2). 

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