A central limit theorem for random tangent fields on stratified spaces

Abstract

Variation of empirical Fréchet 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.

17 pages. v1: This is the third in a four-part series, starting with shadow geometry and geometry of measures on stratified spaces, leading to central limit theorems for Fréchet means on stratified spaces. v2: updated intro and minor corrections. v3: pervasive notational error fixed and other minor improvements