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

doi:10.1090/proc/15429

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

Authors

Benjamin Eltzner

Professor Fernando Galaz Garcia fernando.galaz-garcia@durham.ac.uk
Associate Professor

Stephan F. Huckemann

Wilderich Tuschmann

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