We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Barycenters and a law of large numbers in Gromov hyperbolic spaces.
- Authors
Shin-ichi Ohta
- 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.
- Subjects
PROBABILITY measures; METRIC spaces; HYPERBOLIC groups
- Publication
Revista Mathematica Iberoamericana, 2024, Vol 40, Issue 3, p1185
- ISSN
0213-2230
- Publication type
Article
- DOI
10.4171/RMI/1483