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تسجيل مستخدم جديدCharacterization of a class of weak transport-entropy inequalities on the line
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Nathael Gozlan
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We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost function. As an application, we give a necessary and sufficient condition for weak transport-entropy inequalities in dimension one. In particular, we obtain a weak transport-entropy form of the convex Poincar{e} inequality in dimension one.
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