Michael Goldman

Exact Asymptotics for the 2D Euclidean Random Matching Problem

We determine the exact first-order asymptotics of the expected optimal cost in two-dimensional random bipartite matching, for every finite power cost $q \ge 1$, on the flat torus. In the endpoint case $q=1$, this answers a question by Talagrand, in the periodic case. The argument involves the closely related asymptotic...