Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT

TL;DR

This paper studies entropy-penalized Wasserstein barycenters, characterizing their PDE structure, establishing regularity and moment bounds, and proving a central limit theorem for these barycenters.

Contribution

It provides a PDE-based characterization, regularity results, and a CLT for entropy-penalized Wasserstein barycenters, extending prior work on their properties.

Findings

Characterization via Monge-Ampère equations

Global moment and Sobolev bounds established

Central limit theorem proved for entropic-Wasserstein barycenters

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.