Timeline for When do $\phi^2$ and $\phi’^2$ have the same expectation under a Gaussian random variable?
Current License: CC BY-SA 4.0
8 events
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| Apr 27, 2020 at 4:52 | comment | added | user3750444 | @NateEldredge Thank you very much! I will cite your answer in my paper. | |
| Feb 1, 2020 at 2:45 | comment | added | Nate Eldredge | @user3750444: I mean that we have $\operatorname{Var}[f(Z)] = E[f'(Z)^2]$ if and only if $f$ is linear. $\phi(x) = \exp(x)$ does not have a unique $c$; following the calculation above shows that $\phi(x) = \exp(x) - 2e^{1/2}$ also works. | |
| Feb 1, 2020 at 2:39 | vote | accept | user3750444 | ||
| Feb 1, 2020 at 2:09 | comment | added | user3750444 | What do you mean by Poincaré inequality saturates? $\phi(x)=\exp(x)$ is also such a function where $c$ is unique, right? | |
| Jan 30, 2020 at 16:48 | history | edited | Nate Eldredge | CC BY-SA 4.0 |
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| Jan 30, 2020 at 16:38 | comment | added | user44143 | A good online reference seems to be ssk.im/blog/poincare-inequalities | |
| Jan 30, 2020 at 16:31 | history | edited | Nate Eldredge | CC BY-SA 4.0 |
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| Jan 30, 2020 at 16:26 | history | answered | Nate Eldredge | CC BY-SA 4.0 |