Stability of the cut locus and a central limit theorem for Fréchet means of Riemannian manifolds

Eltzner, Benjamin; Galaz-García, Fernando; Huckemann, Stephan; Tuschmann, Wilderich

doi:10.1090/proc/15429

Stability of the cut locus and a central limit theorem for Fréchet means of Riemannian manifolds
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by Benjamin Eltzner, Fernando Galaz-García, Stephan F. Huckemann and Wilderich Tuschmann PDF

Proc. Amer. Math. Soc. 149 (2021), 3947-3963 Request permission

Abstract:

We obtain a central limit theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin’s Omnibus central limit theorem for Fréchet means. We obtain our CLT assuming certain stability hypothesis for the cut locus, which always holds when the manifold is compact but may not be satisfied in the non-compact case.

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