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 $(X_{1},\ldots,X_{n})$, where $X_{i}$’s are independent real random variables whose tails satisfy certain exponential type decay condition.
Citation
Naomi Feldheim. Arnaud Marsiglietti. Piotr Nayar. Jing Wang. "A note on the convex infimum convolution inequality." Bernoulli 24 (1) 257 - 270, February 2018. https://doi.org/10.3150/16-BEJ875
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