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Simplify Wasserstein distance between Gaussians with binary cost function

Let $\mu_1$ and $\mu_2$ be 1D gaussian distributions with means $m_1$ and $m_2$ respectively and common variance $\sigma$. Let $\Omega$ be a closed subset of $\mathbb R^2$, and consider the cost ...
dohmatob's user avatar
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Is integration against an indicator Wasserstein-Continuous

Let $\mathcal{P}_p(X)$ denote the Wasserstein space over a compact metric space $X$, and $1\leq p<\infty$. Fix a non-empty closed subset $C\subseteq X$. Then is the map: $$ \mathbb{P} \mapsto \...
ABIM's user avatar
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