A Criterion for Talagrand’s Quadratic Transportation Cost Inequality
نویسنده
چکیده
Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré 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 [6], that are shown to hold as soon as a Poincaré inequality is satisfied.
منابع مشابه
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