Timeline for Distance between root of $f$ and its Gaussian convolution
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2023 at 18:47 | comment | added | NancyBoy | Thank you very much ! | |
| Aug 7, 2023 at 18:46 | vote | accept | NancyBoy | ||
| Aug 7, 2023 at 18:44 | comment | added | Iosif Pinelis | This is now done. | |
| Aug 7, 2023 at 18:44 | answer | added | Iosif Pinelis | timeline score: 3 | |
| Aug 7, 2023 at 15:31 | comment | added | NancyBoy | Thank you @IosifPinelis, it will be perfect ! | |
| Aug 7, 2023 at 14:50 | comment | added | Iosif Pinelis | I think it can be shown that under minimal suitable conditions on $f$ we have $\lambda_\sigma\sim-\dfrac{f''(0)}{2f'(0)}\,\sigma^2$ as $\sigma\downarrow0$. If this is enough for you, I can try to write it up. | |
| Aug 7, 2023 at 14:38 | comment | added | NancyBoy | @IosifPinelis, Thank you for your example, is there a more general formula depending on $f$ and $\sigma$ ? | |
| Aug 7, 2023 at 14:15 | comment | added | NancyBoy | Thank you @IosifPinelis, I had edited my post and it didn't make any sense. Now I corrected it. I am looking for the difference between the zero of a function, and the zero of its gaussian convolution. | |
| Aug 7, 2023 at 14:13 | history | edited | NancyBoy | CC BY-SA 4.0 |
added 15 characters in body
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| Aug 7, 2023 at 14:03 | comment | added | Iosif Pinelis | What is $x^*_\sigma$? Is it $\lambda_\sigma$? Also, how come "linear in $\sigma$"? If e.g. $f(x)=e^x-1$, then $\lambda_\sigma=-\sigma^2/2$. | |
| Aug 7, 2023 at 13:00 | history | edited | NancyBoy | CC BY-SA 4.0 |
added 39 characters in body; edited tags
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| S Aug 7, 2023 at 12:51 | review | First questions | |||
| Aug 7, 2023 at 13:10 | |||||
| S Aug 7, 2023 at 12:51 | history | asked | NancyBoy | CC BY-SA 4.0 |