For Gaussian measures, the two Wasserstein projections in the convex order are explicit functions of the covariance matrices, and non-uniqueness occurs only in a characterized singular case.
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Wasserstein projections in the convex order: regularity and characterization in the quadratic Gaussian case
For Gaussian measures, the two Wasserstein projections in the convex order are explicit functions of the covariance matrices, and non-uniqueness occurs only in a characterized singular case.