Representation of Wasserstein distance in terms of CDF

[AdrienCorenflos]

Hello,

Thanks a lot for making these notes available, I'm only at Chapter 2 already am learning a lot from them! I noticed a mistake in your description of W_k^k in terms of the difference of CDFs Ch2 p18, which is only true for k=1, otherwise this needs to be the kth-power of the difference between the quantile functions. You can for example see Remark 2.30 in Cuturi and Peyré Computational Optimal Transport book.

Adrien