Barycenters and a law of large numbers in Gromov hyperbolic spaces

We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces. We establish a contraction property (the Wasserstein distance between probability measures provides an upper bound of the distance between their b...

Full description

Saved in:
Bibliographic Details
Published inRevista matemática iberoamericana Vol. 40; no. 3; pp. 1185 - 1206
Main Author Ohta, Shin-ichi
Format Journal Article
LanguageEnglish
Spanish
Published European Mathematical Society Publishing House 01.06.2024
Subjects
Analysis
Mathematical optimization
Online AccessGet full text

Cover

More Information
Summary:We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces. We establish a contraction property (the Wasserstein distance between probability measures provides an upper bound of the distance between their barycenters), a deterministic approximation of barycenters of uniform distributions on finite points, and a kind of law of large numbers. These generalize the corresponding results on CAT(0)-spaces, up to additional terms depending on the hyperbolicity constant.
ISSN:0213-2230
2235-0616
DOI:10.4171/RMI/1483