Kantorovich duality for general transport costs and applications

• Published in: Journal of functional analysis Vol. 273; no. 11; pp. 3327 - 3405
• Main Authors: Gozlan, Nathael, Roberto, Cyril, Samson, Paul-Marie, Tetali, Prasad
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2017
• Subjects: Duality; Logarithmic-Sobolev inequalities; Metric spaces; Transport inequalities; 60E15; 32F32; Transport inequalities; 26D10; Duality; Metric spaces; Logarithmic-Sobolev inequalities

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. As a by-product we obtain various applications...