Characterizations of B-valued concentration inequalities via the Rademacher type

被引：0

作者：

Cheng, Lixin ^{[1
]}

He, Wuyi ^{[1
]}

Luo, Sijie ^{[2
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen, Peoples R China

[2] Cent South Univ, Sch Math & Stat, Changsha, Peoples R China

来源：

JOURNAL OF TOPOLOGY AND ANALYSIS | 2024年 / 16卷 / 05期

关键词：

Probability measure; concentration inequality; Rademacher type; Banach space;

D O I：

10.1142/S1793525323500061

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that a sufficient and necessary condition for that the Hoeffding concentration inequality of Banach space-valued (B-valued, for simplicity) random variables holds is that the Banach space in question admits the Rademacher type p for some 1 <= p <= 2; which is equivalent to that the Bernstein concentration inequality holds for such B-valued random variables. This is done by applying a refined McDiarmid inequality (stated and proved in this paper) via the entropy method. This result is also applied to the density property of induced subgraphs of random Cayley graphs generated by a finite abelian group.

引用

页码：877 / 904

页数：28

共 31 条

[21] On the role of convexity in isoperimetry, spectral gap and concentration [J].