Submitted Paper
Inserted: 29 sep 2006
Year: 2006
Abstract:
We study monotonicity properties for minimizers of transport problems. In the one-dimensional case, we present an algorithm to construct minimizing monotone transport plans by ``monotonizing'' a given minimizing transport plan. This method applies in particular to the case of the $L^1$-Wasserstein metric where we prove the existence of monotone minimizers for arbitrary marginals. We find that monotone transport plans are in a certain sense close to monotone transport maps.
Keywords: Wasserstein distance, cyclical monotonicity, transport problems, covariance
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