Log-majorization and Lie-Trotter formula for the Cartan barycenter on probability measure spaces

DOI10.1016/j.jmaa.2017.03.027zbMath1365.15023arXiv1609.08909OpenAlexW2964264583MaRDI QIDQ2396861

Yongdo Lim, Fumio Hiai

Publication date: 26 May 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08909

zbMATH Keywords

positive definite matrixunitarily invariant normWasserstein distanceCartan barycenterlog-majorizationLie-Trotter formula

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (10)

Repetition invariant geometric means ⋮ Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter ⋮ Some matrix inequalities of log-majorization type ⋮ Geometric mean flows and the Cartan barycenter on the Wasserstein space over positive definite matrices ⋮ Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices ⋮ The quasi-arithmetic means and Cartan barycenters of compactly supported measures ⋮ Matrix-valued Jensen's inequality and its application to eigenvalue analysis ⋮ Operator means of probability measures ⋮ Ando–Hiai type inequalities for multivariate operator means ⋮ Operator means deformed by a fixed point method

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