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arXiv · 2012.10701

Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT

Guillaume Carlier·Katharina Eichinger·Alexey Kroshnin
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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.

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Guillaume Carlier, Katharina Eichinger, Alexey Kroshnin. 2020-12-19. Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT. https://doi.org/10.1137/20m1387262

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