Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices

DOI10.1016/j.jmaa.2017.10.055zbMath1379.65007OpenAlexW2767874346MaRDI QIDQ1684713

Yongdo Lim

Publication date: 12 December 2017

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.10.055

zbMATH Keywords

positive definite matrixprobability measuresstochastic approximationsWasserstein distancecontractive barycenterThompson metric\(L^1\) ergodic theoremCartan meanCartan-Hadamard metric

Mathematics Subject Classification ID

Related Items (4)

Repetition invariant geometric means ⋮ Mixture and interpolation of the parameterized ordered means ⋮ A Proximal Average for Prox-Bounded Functions ⋮ Convergence theorems for barycentric maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonexpansiveness of the resolvent average
• Approximations to the Karcher mean on Hadamard spaces via geometric power means
• The matrix geometric mean of parameterized, weighted arithmetic and harmonic means
• Monotonic properties of the least squares mean
• Matrix power means and the Karcher mean
• Stability of a 4th-order curvature condition arising in optimal transport theory
• Extending Lipschitz and Hölder maps between metric spaces
• Convexity of the geodesic distance on spaces of positive operators
• Extending Lipschitz functions via random metric partitions
• Generalization of the Hilbert metric to the space of positive definite matrices
• Optimal transportation with infinitely many marginals
• Ordered probability spaces
• The resolvent average for positive semidefinite matrices
• Log-majorization and Lie-Trotter formula for the Cartan barycenter on probability measure spaces
• Karcher means and Karcher equations of positive definite operators
• Spectral calculus and Lipschitz extension for barycentric metric spaces
• Nonlinear Perron–Frobenius Theory
• A CAT(0)-VALUED POINTWISE ERGODIC THEOREM
• Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem
• A general framework for extending means to higher orders
• The $\infty$-Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps
• The Proximal Average: Basic Theory
• Riemannian center of mass and mollifier smoothing
• An L¹ ergodic theorem with values in a non-positively curved space via a canonical barycenter map
• Contractive barycentric map
• Weighted means and Karcher equations of positive operators
• A geometric path from zero Lyapunov exponents to rotation cocycles
• Weighted deterministic walks for the least squares mean on Hadamard spaces
• How to Transform One Convex Function Continuously into Another
• On Certain Contraction Mappings in a Partially Ordered Vector Space

This page was built for publication: Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices