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Barycenters and a law of large numbers in Gromov hyperbolic spaces.
- Source :
-
Revista Mathematica Iberoamericana . 2024, Vol. 40 Issue 3, p1185-1206. 22p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PROBABILITY measures
*METRIC spaces
*HYPERBOLIC groups
Subjects
Details
- Language :
- English
- ISSN :
- 02132230
- Volume :
- 40
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Revista Mathematica Iberoamericana
- Publication Type :
- Academic Journal
- Accession number :
- 177019822
- Full Text :
- https://doi.org/10.4171/RMI/1483