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

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

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.

Citation

Eltzner, B., Galaz-García, F., Huckemann, S. F., & Tuschmann, W. (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. https://doi.org/10.1090/proc/15429

• Journal Article Type: Article
• Acceptance Date: Oct 21, 2020
• Online Publication Date: Jun 18, 2021
• Publication Date: 2021
• Deposit Date: Nov 1, 2020
• Publicly Available Date: Jul 28, 2021
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 149
• Issue: 9
• Pages: 3947-3963
• DOI: https://doi.org/10.1090/proc/15429