Open Access
2012 Transport-Entropy inequalities on the line
Nathael Gozlan
Author Affiliations +
Electron. J. Probab. 17: 1-18 (2012). DOI: 10.1214/EJP.v17-1864


We give a necessary and sucient condition for transport entropy inequalities in dimension one. As an application, we construct a new example of a probability distribution verifying Talagrand's $T_2$ inequality and not the logarithmic Sobolev inequality.


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Nathael Gozlan. "Transport-Entropy inequalities on the line." Electron. J. Probab. 17 1 - 18, 2012.


Accepted: 29 June 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1260.60029
MathSciNet: MR2946156
Digital Object Identifier: 10.1214/EJP.v17-1864

Primary: 60E15
Secondary: 26D10

Keywords: Optimal transport , Poincaré inequality , Transport-entropy inequalities

Vol.17 • 2012
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