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Orthogonality in Wasserstein tangent space for discrete measures with equal mass
Let say I have $N$ discrete probability measures $(\mu_1,...,\mu_N)$ where each of them has $n$ points in $\mathbb{R}^2$ of equal mass.
Let $P(\mathcal{X})$ be the space of these probability measures ...
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Tangent space and gradient on subspace of Wasserstein space given by finitely supported measures
Let $\mathcal{P}_2(M)$ be the 2-Wasserstein space over some Riemannian manifold $(M,g)$ (connected, complete, and without boundary). Let $\mathcal{FP}_2(M,n)$ be the subspace of probability measures ...