2014/03/14 by Larsson, Joel · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1403.3635
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 π2/6 in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension q ≥ 1, such as Wei(1,q) costs. In this paper we extend those results all q>0, confirming the Mézard-Parisi conjecture in the last remaining applicable case.