Timeline for Wasserstein bounds of interpolation measures
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 12 at 14:54 | comment | added | leo monsaingeon | I presume $p_0,p_1$ share the same support? otherwise mass should "jump" infinitely fast whenever vacuum must be filled (either at $t=0^+$ ot $t=1^-$) and this should lead to non-absolute continuity in time (in the $W_2$ distance) | |
| Apr 22 at 16:55 | comment | added | mathguy23123 | I would guess the mildest assumption is something along the lines of bounded moments. However, I expect more regularity to be needed.This could be in the form of Sobolev regularity of $p_0$ and $p_1$. Such bounds do hold true by the way for the geodesic paths, see e.g., the book of Ambrosio. | |
| Apr 22 at 16:53 | history | edited | mathguy23123 | CC BY-SA 4.0 |
added 316 characters in body
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| Apr 22 at 16:51 | comment | added | Liding Yao | So what do people usually assume? Say $L^2$, $L^1$ or Schawartz, or some Sobolev spaces? | |
| Apr 22 at 16:51 | comment | added | mathguy23123 | I will add the definition of the Wasserstein distance. For the densities, this I do not know yet, I am not even sure under which conditions these bounds hold true. | |
| Apr 22 at 16:48 | comment | added | Liding Yao | It's good if you put the definition of what assumption you have on densities and the definition of Wasserstein distance to the question. | |
| S Apr 22 at 16:25 | review | First questions | |||
| Apr 22 at 16:48 | |||||
| S Apr 22 at 16:25 | history | asked | mathguy23123 | CC BY-SA 4.0 |