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Results tagged with wasserstein-distance
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user 163454
2
votes
1
answer
282
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Upper bound Wasserstein distance by $\chi^2$ distance
Given two random variables $X,Y$ which are both $\mathbb{N}$-valued and have the same expected value (which is some fixed positive constant), and denote their probability mass functions by ${\bf p} = …
- 730
1
vote
1
answer
277
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Bounding $2$-Wasserstein distance and the $L^1$ distance
My questions come from the paper Logarithmic Sobolev inequalities for some
nonlinear PDE’s written by F. Malrieu (May 2001) where author omitted a good amount of details to be filled. Suppose that $W$ …
- 730
1
vote
1
answer
390
views
Derivative of Wasserstein distance $W^p_p$ along solutions of the continuity equation (contr...
Let $(\rho^{(i)}_t,{\bf v}^{(i)}_t)$ for $i = 1,2$ be two solutions of the continuity equation $$\partial \rho^{(i)}_t + \nabla\cdot \left({\bf v}^{(i)}_t \rho^{(i)}_t\right) = 0 \label{1}\tag{1}$$ on …
- 730