For simultaneous optimal transport, the paper proves existence, characterizes discrete optimal mixing points, and claims Monge and Kantorovich solutions coincide when density ratios are simple functions, but that claim fails for singular measures.
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On a problem of optimal mixing
For simultaneous optimal transport, the paper proves existence, characterizes discrete optimal mixing points, and claims Monge and Kantorovich solutions coincide when density ratios are simple functions, but that claim fails for singular measures.