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arXiv · 2211.00193

Barycenters and a law of large numbers in Gromov hyperbolic spaces

Shin-ichi Ohta
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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.

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Shin-ichi Ohta. 2022-10-31. Barycenters and a law of large numbers in Gromov hyperbolic spaces. https://arxiv.org/abs/2211.00193

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