Title: Central Limit Theorem for empirical transportation cost in general dimension,
Abstract: We consider the problem of optimal transportation with quadratic cost between
a empirical measure and a general target probability on R d , with d $\ge$ 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 distributions are Gaussian and admit a
simple description in terms of the optimal transportation potentials.