Central limit theorems for empirical transportation cost in general dimension

Eustasio del Barrio, Jean-Michel Loubes
2019 Annals of Probability  
We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d ≥ 1. We provide new results on the uniqueness and stability of the associated optimal transportation potentials, namely, the minimizers in the dual formulation of the optimal transportation problem. As a consequence, we show that a CLT holds for the empirical transportation cost under mild moment and smoothness requirements. The limiting
more » ... are Gaussian and admit a simple description in terms of the optimal transportation potentials.
doi:10.1214/18-aop1275 fatcat:dsgl73m4ubfz7orp5xrv76ozty