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

Sergey G. Bobkov; Piotr Nayar; Prasad Tetali

doi:10.1007/978-3-319-45282-1_3

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 proceeding › Chapter

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 σ² (μ_A) ≤ c log e/μ.(A)) σ²(μ), where μ_A 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)
Title of host publication	Lecture Notes in Mathematics
Publisher	Springer Verlag
Pages	25-53
Number of pages	29
DOIs	https://doi.org/10.1007/978-3-319-45282-1_3
State	Published - 2017

Publication series

Name	Lecture Notes in Mathematics
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.

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© Springer International Publishing AG 2017.

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title = "Concentration properties of restricted measures with applications to non-Lipschitz functions",

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.",

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doi = "10.1007/978-3-319-45282-1_3",

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T1 - Concentration properties of restricted measures with applications to non-Lipschitz functions

AU - Bobkov, Sergey G.

AU - Nayar, Piotr

AU - Tetali, Prasad

N1 - 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.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

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M3 - Chapter

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SP - 25

EP - 53

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -

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

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