Law of large numbers in CAT(1)-spaces of small radii

DOI10.1007/s00526-018-1310-5zbMath1395.53048OpenAlexW2790671902MaRDI QIDQ1751573

Takumi Yokota

Publication date: 25 May 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-018-1310-5

zbMATH Keywords

law of large numbersAlexandrov geometry

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items

Old and new challenges in Hadamard spaces ⋮ Stability of RCD condition under concentration topology ⋮ Strong law of large numbers for the \(L^1\)-Karcher mean

Cites Work

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• Convex functions and barycenter on CAT(1)-spaces of small radii
• Means in metric spaces and the center of mass
• Rate of convergence of stochastic processes with values in \(\mathbb {R}\)-trees and Hadamard manifolds
• Discrete-time gradient flows and law of large numbers in Alexandrov spaces
• Equilibrium maps between metric spaces
• Convex functions and \(p\)-barycenter on CAT(1)-spaces of small radii
• Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature
• The proximal point algorithm in metric spaces
• Convexities of metric spaces
• Computing Medians and Means in Hadamard Spaces
• Riemannian $L^{p}$ center of mass: Existence, uniqueness, and convexity
• Convexity and the Hemisphere
• Real Analysis and Probability
• An L¹ ergodic theorem with values in a non-positively curved space via a canonical barycenter map
• Gradient flows and a Trotter-Kato formula of semi-convex functions on CAT(1)-spaces
• Weighted deterministic walks for the least squares mean on Hadamard spaces
• Convergence of weighted averages of random variables revisited