Timeline for How is this bound for a Wasserstein contraction coefficient in this paper obtained?
Current License: CC BY-SA 4.0
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| Jun 14, 2020 at 6:15 | comment | added | 0xbadf00d | They proceed in the proof of Lemma 3.8 by showing a rather simple inequality: i.sstatic.net/hJRkW.png. It seems like they are claiming that $$1-\alpha_\ast+\alpha_\ast d(x,y)\le\frac{1+\alpha_\ast\beta K_\ast}{1+\beta K_\ast}d(x,y),$$ but I'm not able to see how they obtain this. They say that it follows from $d(x,y)\ge1+\beta K_\ast$ and so I've tried to add $d(x,y)-(1+\beta K_\ast)\ge0$ to the right-hand side. However, I wasn't able to arrange the terms so that they match the right-hand side. Do you've got an idea? | |
| Jun 13, 2020 at 18:51 | vote | accept | 0xbadf00d | ||
| Jun 13, 2020 at 18:51 | comment | added | LL 3.14 | Yes, corrected ;) | |
| Jun 13, 2020 at 18:51 | history | edited | LL 3.14 | CC BY-SA 4.0 |
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| Jun 13, 2020 at 18:37 | comment | added | 0xbadf00d | Thank you for your answer. A few remarks: It should be $K_\ast:=\frac K{\alpha_\ast-\alpha}$, since otherwise $K_\ast$ is negative. And the first inequality in your displaced equation is an equality. | |
| Jun 13, 2020 at 17:40 | history | answered | LL 3.14 | CC BY-SA 4.0 |
