Characterization of a class of weak transport-entropy inequalities on the line
Gozlan, Nathael · Roberto, Cyril · Samson, Paul-Marie · Shu, Yan · Tetali, Prasad
Original · EN
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 Poincaré inequality in dimension one.
English translation
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