ETD

• Matching Problem
• Optimal Transport
• Probability

The random matching problem concerns the study of the transportation cost of empirical measures of independent identically distributed random variables towards their common law.
Working on a 2-dimensional manifold with cost given by the quadratic Wasserstein distance $W^2_2$, we describe an improvement over the technique by Ambrosio, Stra, Trevisan to compute the asymptotic rate of the expected cost. Furthermore, we outline a new optimality condition for transport maps on manifolds.