Transport-Entropy inequalities on the line

Nathael Gozlan (Université Marne-la-Vallée)


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 T2 inequality and not the logarithmic Sobolev inequality.

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Pages: 1-18

Publication Date: June 29, 2012

DOI: 10.1214/EJP.v17-1864


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