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arXiv · 1909.00410

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

Benjamin Eltzner·Fernando Galaz-Garcia·Stephan F. Huckemann·Wilderich Tuschmann
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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 Fr\'echet 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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Benjamin Eltzner, Fernando Galaz-Garcia, Stephan F. Huckemann, Wilderich Tuschmann. 2019-09-01. Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds. https://arxiv.org/abs/1909.00410

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