Timeline for Integrability of Gaussian sums
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 16, 2020 at 1:59 | comment | added | Iosif Pinelis | @FedorPetrov : You are right. I forgot that you are dealing there with the tail probabilities, rather with the quadratic exponential moments. | |
| Nov 15, 2020 at 23:19 | comment | added | Fedor Petrov | @IosifPinelis why entire line? $\lambda$ changes from 0 to $\infty$ | |
| Nov 15, 2020 at 22:44 | comment | added | Iosif Pinelis | @FedorPetrov : You integrate $x\mapsto e^{ax}$ over the entire real line for some real $a$. So, the integral will be $\infty$ no matter whether $a$ is $>0$ or $<0$ or $=0$. | |
| Nov 15, 2020 at 22:15 | comment | added | Fedor Petrov | @IosifPinelis (i) fixed, for (ii) I am not sure, if the average of $\sum \delta_i X_i$ is negative. | |
| Nov 15, 2020 at 22:14 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
added 4 characters in body
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| Nov 15, 2020 at 20:31 | comment | added | Paata Ivanishvili | Or one can write it as $t<\frac{1}{2\min_{\delta \in \{-1,1\}^{n}} \langle \Sigma \delta, \delta \rangle}$ where $\Sigma$ is a covariance matrix of $X=(X_{1}, \ldots, X_{n})$. | |
| Nov 15, 2020 at 20:28 | comment | added | Iosif Pinelis | This is nice. Just wo little things: (i) it is $t<1/(2\sigma^2)$ and $t\ge1/(2\sigma^2)$, rather than $t<2\sigma^2$ and $t\ge2\sigma^2$, and (ii) you cannot take $t=1/(2\sigma^2)$ for any specific $\delta$'s. | |
| Nov 15, 2020 at 20:01 | history | answered | Fedor Petrov | CC BY-SA 4.0 |