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optimum transportation – Are there any outcomes on focus bounds of Wasserstein distances between empirical measures? Answer

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optimum transportation – Are there any outcomes on focus bounds of Wasserstein distances between empirical measures?

I do know there are focus bounds on $W(mu,hat{mu})$ the place $mu$ and $hat{mu}$ are undoubted and empirical distributions respectively, however is there something on the market on $W(mu,nu)$ versus $W(hat{mu},hat{nu})$ the place $hat{mu}$ and $hat{nu}$ are the empirical distributions comparable to $mu$ and $nu$ respectively?

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