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Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT

Carlier, Guillaume; Eichinger, Katharina; Kroshnin, Alexey (2021), Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT, SIAM Journal on Mathematical Analysis, 53, 5, p. 5880–5914. 10.1137/20M1387262

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
SIAM Journal on Mathematical Analysis
Volume
53
Number
5
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
5880–5914
Publication identifier
Metadata
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Eichinger, Katharina
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kroshnin, Alexey
Institut Camille Jordan [ICJ]
Abstract (EN)
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.
Subjects / Keywords
Central limit theorem; Monge-Ampère equations and systems; Entropic-Wasserstein barycenters