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We introduce a general notion of transport cost that encompasses many costs used in the literature (including the classical one and weak transport costs introduced by Talagrand and Marton in the 90's), and prove a Kantorovich type duality theorem.
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N. Gozlan, C. Roberto, P.-M. Samson, Y. Shu, and P. Tetali, Characterization of a class of weak transport-entropy inequalities on the line , Preprint - submitted, 2015
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N. Gozlan, C. Roberto, P.-M. Samson, and P. Tetali, Transport-entropy inequalities for some discrete measures , Preprint, 2016
2016
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