A note on the convex infimum convolution inequality

Naomi Feldheim; Arnaud Marsiglietti; Piotr Nayar; Jing Wang

doi:https://doi.org/10.3150/16-BEJ875

A note on the convex infimum convolution inequality

Naomi Feldheim, Arnaud Marsiglietti, Piotr Nayar, Jing Wang

Research output: Contribution to journal › Article › peer-review

Abstract

We characterize the symmetric real random variables which satisfy the one dimensional convex infimum convolution inequality of Maurey. We deduce Talagrand's two-level concentration for random vector (X1, Xn), where Xi 's are independent real random variables whose tails satisfy certain exponential type decay condition.

Original language	English
Pages (from-to)	257-270
Number of pages	14
Journal	Bernoulli
Volume	24
Issue number	1
DOIs	https://doi.org/10.3150/16-BEJ875
State	Published - Feb 2018
Externally published	Yes

Keywords

Concentration of measure
Convex sets
Infimum convolution
Poincaré inequality
Product measures

All Science Journal Classification (ASJC) codes

Statistics and Probability

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https://doi.org/10.3150/16-BEJ875

Cite this

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title = "A note on the convex infimum convolution inequality",

abstract = "We characterize the symmetric real random variables which satisfy the one dimensional convex infimum convolution inequality of Maurey. We deduce Talagrand's two-level concentration for random vector (X1, Xn), where Xi 's are independent real random variables whose tails satisfy certain exponential type decay condition.",

keywords = "Concentration of measure, Convex sets, Infimum convolution, Poincar{\'e} inequality, Product measures",

author = "Naomi Feldheim and Arnaud Marsiglietti and Piotr Nayar and Jing Wang",

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year = "2018",

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AU - Feldheim, Naomi

AU - Marsiglietti, Arnaud

AU - Nayar, Piotr

AU - Wang, Jing

PY - 2018/2

Y1 - 2018/2

N2 - We characterize the symmetric real random variables which satisfy the one dimensional convex infimum convolution inequality of Maurey. We deduce Talagrand's two-level concentration for random vector (X1, Xn), where Xi 's are independent real random variables whose tails satisfy certain exponential type decay condition.

AB - We characterize the symmetric real random variables which satisfy the one dimensional convex infimum convolution inequality of Maurey. We deduce Talagrand's two-level concentration for random vector (X1, Xn), where Xi 's are independent real random variables whose tails satisfy certain exponential type decay condition.

KW - Concentration of measure

KW - Convex sets

KW - Infimum convolution

KW - Poincaré inequality

KW - Product measures

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U2 - https://doi.org/10.3150/16-BEJ875

DO - https://doi.org/10.3150/16-BEJ875

M3 - مقالة

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VL - 24

SP - 257

EP - 270

JO - Bernoulli

JF - Bernoulli

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A note on the convex infimum convolution inequality

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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