The minimum perfect matching in pseudo-dimension 0

Abstract

It is known that for Kn, n equipped with i.i.d. exp (1) edge costs, the minimum total cost of a perfect matching converges to ζ (2)=π2/6 in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension q≥ 1. In this paper we extend those results to all real positive q, confirming the Mézard-Parisi conjecture in the last remaining applicable case.