Open Access
February 2018 A note on the convex infimum convolution inequality
Naomi Feldheim, Arnaud Marsiglietti, Piotr Nayar, Jing Wang
Bernoulli 24(1): 257-270 (February 2018). DOI: 10.3150/16-BEJ875


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 $(X_{1},\ldots,X_{n})$, where $X_{i}$’s are independent real random variables whose tails satisfy certain exponential type decay condition.


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Naomi Feldheim. Arnaud Marsiglietti. Piotr Nayar. Jing Wang. "A note on the convex infimum convolution inequality." Bernoulli 24 (1) 257 - 270, February 2018.


Received: 1 October 2015; Revised: 1 April 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778327
MathSciNet: MR3706756
Digital Object Identifier: 10.3150/16-BEJ875

Keywords: concentration of measure , convex sets , infimum convolution , Poincaré inequality , product measures

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 1 • February 2018
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