Abstract
We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on $\mathbb{R}^{d}$, with $d\geq1$. 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 distributions are Gaussian and admit a simple description in terms of the optimal transportation potentials.
Citation
Eustasio del Barrio. Jean-Michel Loubes. "Central limit theorems for empirical transportation cost in general dimension." Ann. Probab. 47 (2) 926 - 951, March 2019. https://doi.org/10.1214/18-AOP1275
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