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Apr 22, 2019 at 2:21 answer added Wuchen Li timeline score: 2
Oct 9, 2018 at 0:18 history edited Michael Hardy CC BY-SA 4.0
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Aug 12, 2018 at 1:15 comment added dohmatob Also, Amari's works (e.g fluid.ippt.gov.pl/bulletin/%2858-1%29183.pdf) also appear to be good reference on the 2nd question (the answer is mostly positive).
Aug 11, 2018 at 13:30 comment added dohmatob Talking to a colleague, it appears that Infinitesimally, $W_2$ at a measure $p_\theta$ matches at 2nd order the negative Sobolev space $H^{-1}(dp_\theta)$. This is explained in section 5.5.2 of Santambrogio OTAM book.
Aug 10, 2018 at 0:20 answer added Gabe K timeline score: 3
Aug 9, 2018 at 18:33 history edited dohmatob CC BY-SA 4.0
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Aug 9, 2018 at 16:19 history edited dohmatob CC BY-SA 4.0
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Aug 9, 2018 at 15:50 history edited dohmatob CC BY-SA 4.0
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Aug 9, 2018 at 14:06 history asked dohmatob CC BY-SA 4.0