Stability of the Cut Locus and a Central Limit Theorem for Fr 'echet\n Means of Riemannian Manifolds

2019/09/01 by Benjamin Eltzner, Fernando Galaz‐García, Eltzner, Benjamin +5 · 1 citation
Mathematics · #53C20 #60F05 #62E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Numerical methods in inverse problems #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1909.00410

openalex publication_date 2019/09/01 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We obtain a Central Limit Theorem for closed Riemannian manifolds, clarifying\nalong the way the geometric meaning of some of the hypotheses in Bhattacharya\nand Lin's Omnibus Central Limit Theorem for Fr 'echet means. We obtain our CLT\nassuming certain stability hypothesis for the cut locus, which always holds\nwhen the manifold is compact but may not be satisfied in the non-compact case.\n

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• Zero Probability of the Cut Locus of a Fréchet Mean on a Riemannian Manifold

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