Multimarginal Optimal Transport Maps for One–dimensional Repulsive Costs

By Maria Colombo, L. De Pascale, Simone Di Marino. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2015

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Existence, duality, and cyclical monotonicity for weak transport costs (2018, background): “More recently, variants of this ‘monotonicity priniciple’ have been applied in transport problems for finitely or infinitely many marginals [25, 13, 20, 7, 37], the martingale version of the optimal transport problem [8, 24, 9], the Skorokhod embedding problem [6] and the distribution constrained op”
Applications of weak transport theory (2020, unknown): “More recently, variants of this ‘monotonicity priniciple’ have been applied in transport problems for finitely or infinitely many marginals, the martingale version of the transport problem, the Skorokhod embedding problem, and the distribution constrained optimal stopping problem, see [43, 21, 35, 1”