Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT
Analysis of PDEs
2025-02-04 v2 Probability
Abstract
In this paper, we investigate properties of entropy-penalized Wasserstein barycenters introduced by Bigot, Cazelles and Papadakis (2019) as a regularization of Wasserstein barycenters first presented by Agueh and Carlier (2011). After characterizing these barycenters in terms of a system of Monge-Amp\`ere equations, we prove some global moment and Sobolev bounds as well as higher regularity properties. We finally establish a central limit theorem for entropic-Wasserstein barycenters.
Cite
@article{arxiv.2012.10701,
title = {Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT},
author = {Guillaume Carlier and Katharina Eichinger and Alexey Kroshnin},
journal= {arXiv preprint arXiv:2012.10701},
year = {2025}
}
Comments
46 pages, accepted in SIMA