Barycenters and a law of large numbers in Gromov hyperbolic spaces

Autor:	Ohta, Shin-ichi
Rok vydání:	2022
Předmět:	Mathematics - Metric Geometry Mathematics - Optimization and Control Mathematics - Probability
Zdroj:	Rev. Mat. Iberoam. 40 (2024), 1185-1206
Druh dokumentu:	Working Paper
Popis:	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. Comment: 22 pages; v2: minor revisions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.00193 Zobrazit plný text záznamu View this record from Arxiv