论文标题
Barycenters和Gromov双曲空间中的大量定律
Barycenters and a law of large numbers in Gromov hyperbolic spaces
论文作者
论文摘要
我们研究了Gromov双曲空间上的概率测量的重中心，以开发此类度量空间中的凸优化。我们建立了一个收缩特性（概率度量之间的Wasserstein距离提供了其Barycenters之间距离的上限），在有限点上均匀分布的Barycenters的确定性近似值以及一种大数量定律。这些将相应的结果推广到CAT（0）空间，最多取决于双曲线常数。
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.
