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Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT

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 نشر من قبل Katharina Eichinger
 تاريخ النشر 2020
  مجال البحث
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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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