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

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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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AU - Nayar, Piotr

AU - Tetali, Prasad

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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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