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Transport-entropy inequalities on the line

Nathael Gozlan 1 
1 Laboratoire d'Analyse et de Mathématiques Appliquées
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : We give a necessary and sufficient condition for transport-entropy inequalities in dimension one. As an application, we construct a new example of a probability distri- bution verifying Talagrand's T2 inequality and not the logarithmic Sobolev inequality.
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Submitted on : Friday, March 1, 2013 - 2:50:33 AM
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Nathael Gozlan. Transport-entropy inequalities on the line. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2012, 17 (49), pp.1-18. ⟨10.1214/EJP.v17-1864⟩. ⟨hal-00795830⟩



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