Bounds for the Wasserstein mean with applications to the Lie-Trotter mean

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Hwang, Jinmi¹  Kim, Sejong¹ 

[1] Chungbuk Natl Univ, Dept Math, Cheongju 28644, South Korea

关键词: Wasserstein mean;    Cartan mean;    Lie-Trotter mean;   

DOI  :  10.1016/j.jmaa.2019.03.049

来源: Elsevier

【 摘 要 】

Since barycenters in the Wasserstein space of probability distributions have been introduced, the Wasserstein metric and the Wasserstein mean of positive definite Hermitian matrices have been recently developed. In this paper, we explore some properties of Wasserstein mean of positive definite matrices and find bounds for the Wasserstein mean with respect to operator norm and Loewner order. Using bounds for the Wasserstein mean, we verify that the Wasserstein mean is the multivariate Lie-Trotter mean. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free