Timeline for Integrability of Gaussian sums

8 events

when toggle format	what		by	license	comment
Nov 16, 2020 at 19:04	answer	added	valeri		timeline score: 0
S Nov 16, 2020 at 9:03	history	suggested	gmvh		Added top-level tag
Nov 16, 2020 at 8:36	review	Suggested edits
S Nov 16, 2020 at 9:03
Nov 15, 2020 at 20:01	answer	added	Fedor Petrov		timeline score: 2
Nov 15, 2020 at 19:47	comment	added	Iosif Pinelis		When you say "largest", do you mean for a fixed covariance matrix of the $X_i$'s or otherwise?
Nov 15, 2020 at 19:12	comment	added	Paata Ivanishvili		If $X_i$'s are i.i.d. standard Gaussians then $t=\frac{1}{2n}-\varepsilon$ will work for any $\varepsilon>0$. Indeed, $P(Z>\lambda) \lesssim e^{-\lambda^{2}/2n}$ for all $\lambda>0$, so $\mathbb{E} e^{tZ^{2}} = 2t \int_{0}^{\infty}\lambda e^{t\lambda^{2}}P(Z>\lambda)d\lambda \lesssim 2t \int_{0}^{\infty}\lambda e^{t\lambda^{2} - \frac{\lambda^{2}}{2n}}d\lambda<\infty$.
Nov 15, 2020 at 18:15	review	First posts
Nov 15, 2020 at 19:11
Nov 15, 2020 at 18:09	history	asked	Paul	CC BY-SA 4.0