Stability of the cut locus and a central limit theorem for Fréchet means of Riemannian manifolds,Proceedings of the American Mathematical Society

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Stability of the cut locus and a central limit theorem for Fréchet means of Riemannian manifolds
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-06-18 , DOI: 10.1090/proc/15429
Benjamin Eltzner , Fernando Galaz-García , Stephan 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.

中文翻译：

黎曼流形的 Fréchet 均值的切割轨迹稳定性和中心极限定理

摘要：我们得到了闭黎曼流形的中心极限定理，同时阐明了 Bhattacharya 中的一些假设的几何意义和林的 Fréchet 均值的综合中心极限定理。我们得到我们的 CLT 假设切割轨迹的某些稳定性假设，当流形是紧凑的时总是成立，但在非紧凑的情况下可能不满足。

更新日期：2021-07-27

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