Open Access
2019 Non asymptotic variance bounds and deviation inequalities by optimal transport
Kevin Tanguy
Electron. J. Probab. 24: 1-18 (2019). DOI: 10.1214/19-EJP265


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.


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Kevin Tanguy. "Non asymptotic variance bounds and deviation inequalities by optimal transport." Electron. J. Probab. 24 1 - 18, 2019.


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

zbMATH: 07055651
MathSciNet: MR3916333
Digital Object Identifier: 10.1214/19-EJP265

Primary: 26D10 , 60E15 , 60G70

Keywords: functional inequalities , monotone rearrangement , order statistics , superconcentration

Vol.24 • 2019
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