Electronic Journal of Probability

Non asymptotic variance bounds and deviation inequalities by optimal transport

Kevin Tanguy

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The purpose of this note is to show how simple Optimal Transport arguments, on the real line, can be used in Superconcentration theory. This methodology is efficient to produce sharp non-asymptotic variance bounds for various functionals (maximum, median, $l^p$ norms) of standard Gaussian random vectors in $\mathbb{R} ^n$. The flexibility of this approach can also provide exponential deviation inequalities reflecting preceding variance bounds. As a further illustration, usual laws from Extreme theory and Coulomb gases are studied.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 13, 18 pp.

Received: 10 April 2018
Accepted: 5 January 2019
First available in Project Euclid: 20 February 2019

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 26D10: Inequalities involving derivatives and differential and integral operators 60G70: Extreme value theory; extremal processes

functional inequalities monotone rearrangement superconcentration order statistics

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Tanguy, Kevin. Non asymptotic variance bounds and deviation inequalities by optimal transport. Electron. J. Probab. 24 (2019), paper no. 13, 18 pp. doi:10.1214/19-EJP265. https://projecteuclid.org/euclid.ejp/1550653272

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