2026-04-26T21:59:11Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/823972026-03-11T07:42:58Zcom_10324_1151com_10324_931com_10324_894col_10324_1278

Central limit theorems for semi-discrete Wasserstein distances Barrio Tellado, Eustasio del González Sanz, Alberto Loubes, Jean-Michel Estadística Probabilidad Producción Científica We prove a Central Limit Theorem for the empirical optimal transport cost, √nmn+m{Tc(Pn,Qm)−Tc(P,Q)}, in the semi-discrete case, i.e when the distribution P is supported in N points, but without assumptions on Q. We show that the asymptotic distribution is the sup of a centered Gaussian process, which is Gaussian under some additional conditions on the probability Q and on the cost. Such results imply the central limit theorem for the p-Wassertein distance, for p≥1. This means that, for fixed N, the curse of dimensionality is avoided. To better understand the influence of such N, we provide bounds of E|Wpp(P,Qm)−Wpp(P,Q)| depending on m and N. Finally, the semi-discrete framework provides a control on the second derivative of the dual formulation, which yields the first central limit theorem for the optimal transport potentials and Laguerre cells. The results are supported by simulations that help to visualize the given limits and bounds. We analyse also the cases where classical bootstrap works. 2026-01-30T10:40:15Z 2026-01-30T10:40:15Z 2024 info:eu-repo/semantics/article Bernoulli 30 (1) 554 - 580, February 2024 1350-7265 https://uvadoc.uva.es/handle/10324/82397 10.3150/23-BEJ1608 554 1 580 Bernoulli 30 spa https://projecteuclid.org/journals/bernoulli/volume-30/issue-1/Central-limit-theorems-for-semi-discrete-Wasserstein-distances/10.3150/23-BEJ1608.full info:eu-repo/semantics/restrictedAccess 2024 ISI/BS SI