A new characterization of Talagrand's transport-entropy inequalities and applications

Details A new characterization of Talagrand's transport-entropy inequalities and applications A new characterization of Talagrand's transport-entropy inequalities and applications

2011-04-07

arxiv.org/abs/1104.1303v1

Annals of Probability 2011, Vol. 39, No. 3, 857-880

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP570 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP570

We show that Talagrand's transport inequality is equivalent to a restricted
logarithmic Sobolev inequality. This result clarifies the links between these
two important functional inequalities. As an application, we give the first
proof of the fact that Talagrand's inequality is stable under bounded
perturbations.

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