Monotonicity of transport plans
نویسنده
چکیده
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 L1-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.
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تاریخ انتشار 2006