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 σ2 (μA) ≤ 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 language | English (US) |
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Title of host publication | Lecture Notes in Mathematics |
Publisher | Springer Verlag |
Pages | 25-53 |
Number of pages | 29 |
DOIs | |
State | Published - 2017 |
Publication series
Name | Lecture Notes in Mathematics |
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Volume | 2169 |
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.