Optimal Transport and Wasserstein Barycenter for Radially Contoured Distributions

Understand

The optimal transport and Wasserstein barycenter of Gaussian distributions have been solved.

• In literature, the closed form formulas of the Monge map, the Wasserstein distance and the Wasserstein barycenter have been given.
• Moreover, when Gaussian distributions extend more generally to elliptically contoured distributions, similar results also hold true.
• In this case, Gaussian distributions are regarded as elliptically contoured distribution with generator function $e^{-x/2}$.