Translator Disclaimer
November 2017 The Hoffmann–Jørgensen inequality in metric semigroups
Apoorva Khare, Bala Rajaratnam
Ann. Probab. 45(6A): 4101-4111 (November 2017). DOI: 10.1214/16-AOP1160

Abstract

We prove a refinement of the inequality by Hoffmann–Jørgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space literature, including those by Johnson and Schechtman [Ann. Probab. 17 (1989) 789–808], Klass and Nowicki [Ann. Probab. 28 (2000) 851–862], and Hitczenko and Montgomery-Smith [Ann. Probab. 29 (2001) 447–466]. Finally, we show that the Hoffmann–Jørgensen inequality (including our generalized version) holds not only in Banach spaces but more generally, in a very primitive mathematical framework required to state the inequality: a metric semigroup $\mathscr{G}$. This includes normed linear spaces as well as all compact, discrete or (connected) abelian Lie groups.

Citation

Download Citation

Apoorva Khare. Bala Rajaratnam. "The Hoffmann–Jørgensen inequality in metric semigroups." Ann. Probab. 45 (6A) 4101 - 4111, November 2017. https://doi.org/10.1214/16-AOP1160

Information

Received: 1 May 2016; Revised: 1 October 2016; Published: November 2017
First available in Project Euclid: 27 November 2017

zbMATH: 06838116
MathSciNet: MR3729624
Digital Object Identifier: 10.1214/16-AOP1160

Subjects:
Primary: 60E15
Secondary: 60B15

Rights: Copyright © 2017 Institute of Mathematical Statistics

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.45 • No. 6A • November 2017
Back to Top