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Journal Articles SIAM Journal on Mathematical Analysis Year : 2021

Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT

Abstract

In this paper, we investigate properties of entropy-penalized Wasserstein barycenters introduced in [5] as a regularization of Wasserstein barycenters [1]. After characterizing these barycenters in terms of a system of Monge-Ampère 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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Dates and versions

hal-03084049 , version 1 (20-12-2020)

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Guillaume Carlier, Katharina Eichinger, Alexey Kroshnin. Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT. SIAM Journal on Mathematical Analysis, 2021, ⟨10.1137/20M1387262⟩. ⟨hal-03084049⟩
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