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Register a new userCentral Limit Theorem for empirical transportation cost in general dimension
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Authors
Eustasio Del Barrio
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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.
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