Concentration properties of restricted measures with applications to non-Lipschitz functions

Sergey G. Bobkov, Piotr Nayar, Prasad Tetali

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

We show that, for any metric probability space (M, d, μ) with a subgaussian constant σ2 (μ) and any Borel measurable set A ⊂ M, we have σ2A) ≤ c log e/μ.(A)) σ2(μ), where μA is a normalized restriction of μ to the set A and c is a universal constant. As a consequence, we deduce concentration inequalities for non-Lipschitz functions.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages25-53
Number of pages29
DOIs
StatePublished - 2017

Publication series

NameLecture Notes in Mathematics
Volume2169
ISSN (Print)0075-8434

Bibliographical note

Funding Information:
We would like to thank anonymous referee for pointing out to us several relevant references. S.G. Bobkov’s research supported in part by the Humboldt Foundation, NSF and BSF grants. P. Nayar’s research supported in part by NCN grant DEC-2012/05/B/ST1/00412. P. Tetali’s research supported in part by NSF DMS-1407657.

Publisher Copyright:
© Springer International Publishing AG 2017.

Fingerprint

Dive into the research topics of 'Concentration properties of restricted measures with applications to non-Lipschitz functions'. Together they form a unique fingerprint.

Cite this