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Riemannian submanifolds of $2$-Wasserstein space

Other than point masses in a length space or Gaussian measures in $\mathbb{R}^n$, I don't know of examples of families which are totally geodesic in Wasserstein geometry. However, it is possible to ...
Gabe K's user avatar
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2 votes

Reverse Pinsker's inequality for smooth density classes

The answer is no. E.g., suppose that both $f$ and $g$ are supported on $B=[0,1]$, with $f=1$ on $B$ and $$g(x)=(1-h+x)\,1(0\le x<h)+1(h\le x<1-h)+(x+h)\,1(1-h\le x\le1)$$ for $h\in(0,1/2)$ and $...
Iosif Pinelis's user avatar

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