Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices
type: Item
instance of: scholarly article
title: Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices
zbMATH Open document ID: 1379.65007
author: Yongdo Lim
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-12-12T00:00:00Z
Mathematics Subject Classification ID: 65C50
Mathematics Subject Classification ID: 60A10
zbMATH DE Number: 6817544
zbMATH Keywords: positive definite matrix
zbMATH Keywords: Thompson metric
zbMATH Keywords: Cartan mean
zbMATH Keywords: Wasserstein distance
zbMATH Keywords: contractive barycenter
zbMATH Keywords: \(L^1\) ergodic theorem
zbMATH Keywords: probability measures
zbMATH Keywords: Cartan-Hadamard metric
zbMATH Keywords: stochastic approximations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.10.055
OpenAlex ID: W2767874346
cites work: A CAT(0)-VALUED POINTWISE ERGODIC THEOREM
cites work: The Proximal Average: Basic Theory
cites work: How to Transform One Convex Function Continuously into Another
cites work: The resolvent average for positive semidefinite matrices
cites work: Q3425149
cites work: A geometric path from zero Lyapunov exponents to rotation cocycles
cites work: Q3526643
cites work: The $\infty$-Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps
cites work: Convexity of the geodesic distance on spaces of positive operators
cites work: Q4938944
cites work: Q4321748
cites work: Log-majorization and Lie-Trotter formula for the Cartan barycenter on probability measure spaces
cites work: No dice: a deterministic approach to the Cartan centroid
cites work: Riemannian center of mass and mollifier smoothing
cites work: The matrix geometric mean of parameterized, weighted arithmetic and harmonic means
cites work: Nonexpansiveness of the resolvent average
cites work: Ordered probability spaces
cites work: A general framework for extending means to higher orders
cites work: Monotonic properties of the least squares mean
cites work: Weighted means and Karcher equations of positive operators
cites work: Karcher means and Karcher equations of positive definite operators
cites work: Contractive barycentric map
cites work: Extending Lipschitz functions via random metric partitions
cites work: Nonlinear Perron-Frobenius theory
cites work: Matrix power means and the Karcher mean
cites work: Weighted deterministic walks for the least squares mean on Hadamard spaces
cites work: Approximations to the Karcher mean on Hadamard spaces via geometric power means
cites work: Generalization of the Hilbert metric to the space of positive definite matrices
cites work: Spectral calculus and Lipschitz extension for barycentric metric spaces
cites work: An L1 ergodic theorem with values in a non-positively curved space via a canonical barycenter map
cites work: Extending Lipschitz and Hölder maps between metric spaces
cites work: Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem
cites work: Optimal transportation with infinitely many marginals
cites work: Q4453431
cites work: On Certain Contraction Mappings in a Partially Ordered Vector Space
cites work: Q4805362
cites work: Stability of a 4th-order curvature condition arising in optimal transport theory
DOI: 10.1016/J.JMAA.2017.10.055
description: scientific article; zbMATH DE number 6817544