Timeline for How large are the smallest-area projections of a high-dimensional convex body?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 1, 2014 at 8:14 | comment | added | Pietro Majer | yes, $1/\sqrt{2\pi}$ . | |
| Feb 1, 2014 at 5:57 | comment | added | Alexander Shamov | @PietroMajer: $1/\sqrt{2 \pi}$, I believe. Anyway, $\ell^p$ balls are are certainly not counterexamples. | |
| Jan 31, 2014 at 11:11 | comment | added | Pietro Majer | Among the (normalized) spheres, one actually gets a limit $1/\sqrt{\pi}$ as $d\to\infty$. | |
| Jan 31, 2014 at 9:50 | comment | added | Alexander Shamov | @MarkMeckes: What I wrote at the bottom line made no sense exactly for the reason that you indicated. Please see the updated version. | |
| Jan 31, 2014 at 9:46 | history | edited | Alexander Shamov | CC BY-SA 3.0 |
added 109 characters in body
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| Jan 29, 2014 at 19:22 | comment | added | Alexander Shamov | @MarkMeckes: Homogeneity is not an issue here exactly because of the second moment normalization, i.e. I'm fixing the "width" of the set in any direction. | |
| Jan 29, 2014 at 15:00 | comment | added | Mark Meckes | Are you sure you have the right expression? The homogeneity looks funny. | |
| Jan 26, 2014 at 20:55 | comment | added | Alexander Shamov | @WillSawin: Yes, for the $d$-dimensional cube the largest projection has area of order $\sqrt d$. | |
| Jan 26, 2014 at 20:54 | comment | added | Will Sawin | Is this false with $\sup$ instead of $\inf$? | |
| Jan 26, 2014 at 1:34 | history | asked | Alexander Shamov | CC BY-SA 3.0 |