Timeline for Anti-concentration of the $\ell_2$ norm of log-concave measures
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 26, 2023 at 15:56 | comment | added | Cain | Well, the constant C in Lemma 1 is given explicitly as something which can probably be bounded by 100. The constant C in Lemma 4 is stated to be 4. Now, in the proof of Theorem 4, Case I, they obtain the absolute constant bound C(2e)^(1+1/q), with C the constant from Lemma 4. For Case II, the constant in the first terms can be bounded by 2 times the constant from Lemma 1, so 200. The constant bounding the second term is just the constant from Lemma 4. So, up to bounding the Beta function by q, you should be able to take C = 800 in your question. It is not optimal, but not far from the truth. | |
| Jun 9, 2023 at 17:21 | comment | added | Mark Schultz-Wu | @Cain Maybe, but I am not an analyst, and the disclaimer that "The value of $C$ may change from line to line" has sufficiently intimidated me that determining $C$ may be difficult. | |
| Jun 8, 2023 at 2:30 | comment | added | Cain | Maybe I’m a bit late, but the constants in Lemmas 1 and 4 of the original Carbery Wright paper seem to be explicit enough to get an expression for the cosnstant. | |
| Jan 20, 2023 at 11:50 | history | edited | Mark Schultz-Wu | CC BY-SA 4.0 |
added 136 characters in body
|
| Sep 12, 2022 at 15:58 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
|
| Sep 12, 2022 at 15:21 | history | asked | Mark Schultz-Wu | CC BY-SA 4.0 |