A criterion for Talagrand's quadratic transportation cost inequality

Details A criterion for Talagrand's quadratic transportation cost inequality A criterion for Talagrand's quadratic transportation cost inequality

2003-12-03

arxiv.org/abs/math/0312081v3

Mathematics

Probability

Scientific paper

We show that the quadratic transportation cost inequality $T_2$ is equivalent to both a Poincar\'e inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmic-Sobolev inequalities by Bobkov and Ledoux \cite{BL97}, that are shown to hold as soon as a Poincar\'e inequality is satisfied.

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