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Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds

Eltzner, Benjamin and Galaz-García, Fernando and Huckemann, Stephan F. and Tuschmann, Wilderich (2021) 'Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds.', Proceedings of the American Mathematical Society., 149 (9). 3947-3963 .

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1090/proc/15429
Publisher statement:© Copyright 2021 American Mathematical Society
Date accepted:21 October 2020
Date deposited:28 July 2021
Date of first online publication:18 June 2021
Date first made open access:28 July 2021

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