Central Limit Theorems for Semidiscrete Wasserstein Distances

Eustasio del Barrio, Alberto González-Sanz, Jean-Michel Loubes

We prove a Central Limit Theorem for the empirical optimal transport cost, $\sqrt{\frac{nm}{n+m}}\{{\mathcal{T}}_c(P_n,Q_m)-{\mathcal{T}}_c(P,Q)\}$, in the semi discrete case, i.e when…