The order properties and Karcher barycenters of probability measures on the open convex cone

DOI10.11650/tjm/8117zbMath1505.60007OpenAlexW2745433523MaRDI QIDQ1990368

Sejong Kim

Publication date: 25 October 2018

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.twjm/1502935230

zbMATH Keywords

stochastic orderunitarily invariant normWasserstein distanceLoewner orderKarcher barycentermax-flow and min-cut theorem

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Positive matrices and their generalizations; cones of matrices (15B48) Positive linear operators and order-bounded operators (47B65)

Related Items

Repetition invariant geometric means ⋮ Wasserstein barycenters of compactly supported measures

Cites Work

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• Monotonicity of the matrix geometric mean
• Matrix power means and the Karcher mean
• Operator means of probability measures and generalized Karcher equations
• Ordered cones and approximation
• Log majorization and complementary Golden-Thompson type inequalities
• Convexity of the geodesic distance on spaces of positive operators
• Majorizations and inequalities in matrix theory
• Finsler structures for the part metric and Hilbert's projective metric and applications to ordinary differential equations
• Ordered probability spaces
• Riemannian metrics on positive definite matrices related to means. II
• Positive definite matrices
• Metric convexity of symmetric cones
• Karcher means and Karcher equations of positive definite operators
• Riemannian center of mass and mollifier smoothing
• Contractive barycentric map
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• On Certain Contraction Mappings in a Partially Ordered Vector Space