List questions from optimal-transport

Published on 03 Jun 2021 - 18:48

295

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Directional derivative of $L^2$ wasserstein distance

Published on 09 Jun 2021 - 13:52

1k

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Wasserstein distance between two empirical measures

Published on 13 Jun 2021 - 0:23

417

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Convexity of a set of probability distributions

Published on 17 Jun 2021 - 14:55

63

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Understanding the concept of "dynamical coupling" between measures in the Villani's book

Published on 23 Feb 2026 - 10:19

49

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$\gamma=(Id\times T)_{\#}\mu\implies(x,y)=(x,T(x))$ $\;\gamma$-a.e.

Published on 29 Jun 2021 - 0:48

21

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$\mathcal{J}_c(\mu,\nu)=0\implies\mu=\nu$?

Published on 30 Jun 2021 - 12:27

124

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Fundamental theorem of optimal transport

Published on 05 Jul 2021 - 20:43

36

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$W_2(\mu_t,\mu_s)=\sqrt{|t-s|}d(x,y)$ for $\mu_t:=(1-t)\delta_x+t\delta_y$

Published on 06 Jul 2021 - 15:33

173

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Intuition behind the entropy functional for curvature bounds

Published on 08 Jul 2021 - 14:22

1.4k

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Weak convergence of measures is equivalent to convergence in Wasserstein distance

Published on 09 Jul 2021 - 14:49

48

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How can I evaluate the normed cumulative distribution transform explicitly?

Published on 10 Jul 2021 - 13:20

83

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Pushforward of measures and their support

Published on 14 Jul 2021 - 15:43

126

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Product measure is always an admissible coupling

Published on 15 Jul 2021 - 7:00

370

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The tangent space of the set of measures as a Riemannian manifold

Published on 15 Jul 2021 - 11:01

List Question

Dual solutions of the 1d optimal transport problem

Directional derivative of $L^2$ wasserstein distance

Wasserstein distance between two empirical measures

Convexity of a set of probability distributions

Understanding the concept of "dynamical coupling" between measures in the Villani's book

$\gamma=(Id\times T)_{\#}\mu\implies(x,y)=(x,T(x))$ $\;\gamma$-a.e.

$\mathcal{J}_c(\mu,\nu)=0\implies\mu=\nu$?

Fundamental theorem of optimal transport

$W_2(\mu_t,\mu_s)=\sqrt{|t-s|}d(x,y)$ for $\mu_t:=(1-t)\delta_x+t\delta_y$

Intuition behind the entropy functional for curvature bounds

Weak convergence of measures is equivalent to convergence in Wasserstein distance

How can I evaluate the normed cumulative distribution transform explicitly?

Pushforward of measures and their support

Product measure is always an admissible coupling

The tangent space of the set of measures as a Riemannian manifold

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