E. del Barrio
We consider the problem of optimal transportation with quadratic cost between an 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 distributions are Gaussian and admit a simple description in terms of the optimal transportation potentials.
Palabras clave / Keywords: optimal transportation, optimal matching, CLT, Efron-Stein inequality
Programado
Sesión J01 Probabilidad y Aplicaciones
31 de mayo de 2018 09:00
Sala 4
