Timeline for Chances for a cosine polynomial to be positive at a point
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2014 at 1:23 | comment | added | fedja | If you take several first moments, there are no resonances between frequences, so the moments are exactly the same as for independent random variables, which means that the distributions are close too. | |
| Oct 23, 2014 at 16:41 | comment | added | Liviu Nicolaescu | @fedja Could you elaborate the statement about similarity with the normal distributions? | |
| Oct 23, 2014 at 11:45 | comment | added | fedja | Take a very fast growing sequence of $k_j>0$. Then $f=2s_n/\sqrt{n}$ has essentially standard normal distribution and $f(x)^2-2+n^{-1/2}f(2x)$ has all coefficients equal. However the probability that the standard normal random variable is between $-\sqrt 2$ and $\sqrt 2$ is not $\frac 12$. This shows that we can skew the sign distribution somewhat at any scale. The question is how much... | |
| Oct 23, 2014 at 0:06 | comment | added | fedja | Do you have any particular reason to believe that even, say, $\delta_n=\pi/2$ works for large $n$? | |
| Oct 21, 2014 at 13:43 | answer | added | Liviu Nicolaescu | timeline score: 3 | |
| Oct 21, 2014 at 9:42 | history | edited | TOM | CC BY-SA 3.0 |
added 4 characters in body
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| Oct 21, 2014 at 9:42 | comment | added | TOM | @Liviu Nicolaescu Sorry, $f=s_n$, I corrected the typo. | |
| Oct 21, 2014 at 9:28 | comment | added | Liviu Nicolaescu | Need to explain what is $f$. | |
| Oct 21, 2014 at 8:56 | history | asked | TOM | CC BY-SA 3.0 |