论文标题
熵 - 沃斯坦barycenters：PDE表征，规律性和CLT
Entropic-Wasserstein barycenters: PDE characterization, regularity and CLT
论文作者
论文摘要
在本文中，我们调查了Bigot，Cazelles和Papadakis（2019）引入的熵含量的Wasserstein Barycenters的性质，作为Agueh and Carlier（2011）首次提出的Wasserstein Barycenters的正规化。在以monge-ampère方程式来表征这些bary中心后，我们证明了一定的全球力矩和sobolev界限以及更高的规律性属性。我们终于为熵 - 沃斯坦重中心建立了一个中心限制定理。
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-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.
