Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 49, 18 pp.
Transport-Entropy inequalities on the line
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Abstract
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.
Article information
Source
Electron. J. Probab. Volume 17 (2012), paper no. 49, 18 pp.
Dates
Accepted: 29 June 2012
First available in Project Euclid: 4 June 2016
Permanent link to this document
http://projecteuclid.org/euclid.ejp/1465062371
Digital Object Identifier
doi:10.1214/EJP.v17-1864
Mathematical Reviews number (MathSciNet)
MR2946156
Zentralblatt MATH identifier
1260.60029
Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators
Keywords
Optimal transport Transport-entropy inequalities Poincaré inequality
Rights
This work is licensed under a Creative Commons Attribution 3.0 License.
Citation
Gozlan, Nathael. Transport-Entropy inequalities on the line. Electron. J. Probab. 17 (2012), paper no. 49, 18 pp. doi:10.1214/EJP.v17-1864. http://projecteuclid.org/euclid.ejp/1465062371.
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