Timeline for Constant in Naor and Neiman's Assouad Theorem
Current License: CC BY-SA 4.0
17 events
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| S Sep 4, 2022 at 14:00 | history | bounty ended | CommunityBot | ||
| S Sep 4, 2022 at 14:00 | history | notice removed | CommunityBot | ||
| Aug 28, 2022 at 1:42 | comment | added | ABIM | @VladimirZolotov Both of these comments are rather obvious and the last bit is not very helpful. I'm asking in case someone has computed or knows good estimates on c. | |
| Aug 28, 2022 at 1:39 | history | edited | ABIM | CC BY-SA 4.0 |
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| Aug 27, 2022 at 17:18 | comment | added | Vladimir Zolotov | @AIM Also there is no mystery about this constant(s), You just go through the proof collect all the constant gunk out of every inequality and you get your thing. It's just a tedious and inspiring job. It's hard to imagine somebody will do it for you unless you have some kind of breakthrough application. | |
| Aug 27, 2022 at 15:04 | comment | added | Vladimir Zolotov | @AIM Yeah I see you mean the formulation from Theorem 1.2. But I still think that the part about $N$ could be relevant. At least that what I remember from a more classical Assouad. I mean that you can take a smallish constant in ≲ for $N$ but than you get a big one in ≲ for $D$ and vice versa. | |
| S Aug 27, 2022 at 12:23 | history | bounty started | ABIM | ||
| S Aug 27, 2022 at 12:23 | history | notice added | ABIM | Authoritative reference needed | |
| Aug 27, 2022 at 12:23 | history | edited | ABIM | CC BY-SA 4.0 |
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| Aug 27, 2022 at 12:22 | comment | added | ABIM | @VladimirZolotov Nono I'm referring to the absolute constant $c$ hidden by the $\lesssim$, i can clarify this ofc | |
| Aug 27, 2022 at 9:20 | comment | added | Vladimir Zolotov | For me the question looks very unclear. The constant $D$ depends on $k$ and $\epsilon$ as the abstract says. It also depends on your choice of $N$. There is a tradeoff: you can embed into bigger space with smaller distortion or you can embed in a smaller space but the distortion will be bigger. | |
| Aug 26, 2022 at 7:13 | history | edited | ABIM | CC BY-SA 4.0 |
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| Aug 25, 2022 at 15:06 | comment | added | Aryeh Kontorovich | Should be Naor and Neiman (Ofer is the first name) | |
| Aug 25, 2022 at 11:27 | comment | added | ABIM | @AryehKontorovich done and also fixed the wierd link | |
| Aug 25, 2022 at 11:26 | history | edited | ABIM | CC BY-SA 4.0 |
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| Aug 25, 2022 at 9:15 | comment | added | Aryeh Kontorovich | The link doesn't work. Give a full reference? | |
| Aug 24, 2022 at 23:24 | history | asked | ABIM | CC BY-SA 4.0 |