A central limit theorem for random tangent fields on stratified spaces
Probability
2025-01-07 v3 Metric Geometry
Statistics Theory
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2311.09454,
title = {A central limit theorem for random tangent fields on stratified spaces},
author = {Jonathan C. Mattingly and Ezra Miller and Do Tran},
journal= {arXiv preprint arXiv:2311.09454},
year = {2025}
}
Comments
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 Fr\'echet means on stratified spaces. v2: updated intro and minor corrections. v3: pervasive notational error fixed and other minor improvements