Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field and lays the foundation for more traditionally formulated central limit theorems in subsequent work.

翻译：在曲率有上界的度量空间上，经验弗雷歇均值的变分通过由单位切向量索引的随机场编码。中心极限定理表明这些随机切向场收敛到一个高斯随机场，并为后续工作中更传统形式的中心极限定理奠定了基础。