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A Simple Counterexample to the Monge Ansatz in Multimarginal Optimal Transport, Convex Geometry of the Set of Kantorovich Plans, and the Frenkel--Kontorova Model
It is known from clever mathematical examples [G. Carlier, Lecture Notes IMA, New Mathematical Models in Economics and Finance, (2010), pp. 1--82] that the Monge ansatz may fail in continuous 2-marginal optimal transport (alias optimal coupling alias optimal assignment) problems. Here we show that this effect already occurs for finite …