论文标题
在Stiefel和Grassmann歧管上的高级集中
Higher order concentration on Stiefel and Grassmann manifolds
论文作者
论文摘要
我们证明了具有均匀分布的Stiefel和Grassmann歧管上功能的高阶浓度界限。这部分扩展了对单位球体功能的先前工作。从技术上讲，我们的结果基于对数的Sobolev技术，用于歧管上的均匀度量。应用程序包括Hanson-符合Stiefel歧管的类型不等式和$ \ Mathbb {r}^n $的子空间之间的某些距离功能的浓度界限。
We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work for functions on the unit sphere. Technically, our results are based on logarithmic Sobolev techniques for the uniform measures on the manifolds. Applications include Hanson--Wright type inequalities for Stiefel manifolds and concentration bounds for certain distance functions between subspaces of $\mathbb{R}^n$.
