Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

High Dimensional Probability VIIIMoment Estimation Implied by the Bobkov-Ledoux Inequality

High Dimensional Probability VIII: Moment Estimation Implied by the Bobkov-Ledoux Inequality [In this paper we consider a probability measure on the high dimensional Euclidean space satisfying Bobkov-Ledoux inequality. Bobkov and Ledoux have shown in (Probab Theory Related Fields 107(3):383–400, 1997) that such entropy inequality captures concentration phenomenon of product exponential measure and implies Poincaré inequality. For this reason any measure satisfying one of those inequalities shares the same concentration result as the exponential measure. In this paper using B-L inequality we derive some bounds for exponential Orlicz norms for any locally Lipschitz function. The result is close to the question posted by Adamczak and Wolff in (Probab Theory Related Fields 162:531–586, 2015) regarding moments estimate for locally Lipschitz functions, which is expected to result from B-L inequality.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

High Dimensional Probability VIIIMoment Estimation Implied by the Bobkov-Ledoux Inequality

Part of the Progress in Probability Book Series (volume 74)
Editors: Gozlan, Nathael; Latała, Rafał; Lounici, Karim; Madiman, Mokshay
Bednorz, Witold; Głowienko, Grzegorz
High Dimensional Probability VIII — Nov 27, 2019
Download PDF
11 pages

Loading next page...
 
/lp/springer-journals/high-dimensional-probability-viii-moment-estimation-implied-by-the-huAxwqcx0N

References (4)

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-26390-4
Pages
9 –20
DOI
10.1007/978-3-030-26391-1_2
Publisher site
See Chapter on Publisher Site

Abstract

[In this paper we consider a probability measure on the high dimensional Euclidean space satisfying Bobkov-Ledoux inequality. Bobkov and Ledoux have shown in (Probab Theory Related Fields 107(3):383–400, 1997) that such entropy inequality captures concentration phenomenon of product exponential measure and implies Poincaré inequality. For this reason any measure satisfying one of those inequalities shares the same concentration result as the exponential measure. In this paper using B-L inequality we derive some bounds for exponential Orlicz norms for any locally Lipschitz function. The result is close to the question posted by Adamczak and Wolff in (Probab Theory Related Fields 162:531–586, 2015) regarding moments estimate for locally Lipschitz functions, which is expected to result from B-L inequality.]

Published: Nov 27, 2019

Keywords: Concentration of measure; Poincaré inequality; Sobolev inequality; 60E15; 46N30

There are no references for this article.