optimal transport plan for univariate gaussian

[pparreira]

Hi, I have noticed that the package has the exact optimal transport plan for univariate Gaussian implemented. Before finding your package, I was unable to locate the exact optimal transport plan for univariate Gaussian. Could you please inform me if you used any specific source or if you arrived at the exact solution yourselves?

[zsteve]

For general univariate distributions (including the univariate Gaussian), the p-Wasserstein distance is the Lp-distance between distribution functions, and the corresponding transport map corresponds to quantile matching. You can see e.g. Remarks 2.30, 2.31 of https://arxiv.org/pdf/1803.00567.pdf.