Mathematics Research Institute

Seminario de Doctorado
Seminario de Doctorado

Central limit theorem for general transportation costs

Alberto González Sanz (Universidad de Valladolid)

Fecha: 02/07/2021 13:45
Lugar: Sala de Grados II, Facultad de Ciencias

We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on $\mathbb{R}^{d}$, with $d\geq 1$. We extend results in del Barrio and Loubes and prove asymptotic stability of both optimal transport maps and potentials for a large class of costs in $\mathbb{R}^{d}$. We derive a central limit theorem (CLT) towards a Gaussian distribution for the empirical transportation cost under minimal assumptions, with a new proof based on the Efron-Stein inequality and on the sequential compactness of the closed unit ball in $L_{2}(\mathbb{P})$ for the weak topology.