The minimum perfect matching in pseudo-dimension 0 < q < 1
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 in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension . In this paper we extend those results to all real positive q, confirming the Mézard-Parisi conjecture in the last remaining applicable case.