Timeline for Anti-concentration of Gaussian quadratic form
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2023 at 1:57 | comment | added | dohmatob | See another answer which has optimal dependence on the $a_i$'s mathoverflow.net/a/438937/78539. Basically, you can take $c=r(a)/2$, where $r(a):=\|a\|_1/\|a\|_\infty \ge 1$ with $a=(a_1,\ldots,a_n)$. Note that this choice of $c$ can be much larger than $1/2$, as can be seen when $a_i = 1/n$ for all $i$; here one easily computes $r(a) = n$, and so $c=n/2 = \Omega(n) \gg 1$ for large $n$. | |
| Jan 20, 2023 at 1:27 | answer | added | dohmatob | timeline score: 1 | |
| Aug 16, 2020 at 7:55 | comment | added | dohmatob | Using Chernoff's inequality, you can get the result in one line. See my post below. | |
| Aug 16, 2020 at 7:54 | answer | added | dohmatob | timeline score: 1 | |
| Apr 25, 2012 at 3:30 | vote | accept | Mitch | ||
| Apr 25, 2012 at 2:15 | answer | added | George Lowther | timeline score: 13 | |
| Apr 25, 2012 at 1:44 | answer | added | Ryan O'Donnell | timeline score: 4 | |
| Apr 25, 2012 at 1:12 | comment | added | Mitch | Yes, I would expect $c=1/2,$ but I don't want to discourage somebody with an answer that gives $c<1/2.$ | |
| Apr 25, 2012 at 1:07 | comment | added | George Lowther | Anyway, at first glance it looks like it should hold for $c=1/2$. Is that what you expect, or can you rule that case out? (certainly $c > 1/2$ is ruled out by looking at $n=1$). | |
| Apr 25, 2012 at 0:59 | history | edited | Mitch | CC BY-SA 3.0 |
deleted 13 characters in body
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| Apr 25, 2012 at 0:56 | comment | added | Mitch | No, it's supposed to be an absolute constant independent of $a_1,\dots,a_n$ and $n$. I will update the question. | |
| Apr 25, 2012 at 0:32 | comment | added | George Lowther | Does the implicit constant in $O(\epsilon^c)$ allowed to depend on $n$ and $a_1,\ldots,a_n$? I assume not, but the way it's stated makes it sound like it does to me. | |
| Apr 25, 2012 at 0:17 | history | asked | Mitch | CC BY-SA 3.0 |