Timeline for Is there a determinantal point process proof of the Keating-Snaith formula for the cumulants of the log characteristic polynomial of a random matrix?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 9, 2023 at 11:39 | vote | accept | Will Sawin | ||
| Oct 9, 2023 at 4:41 | answer | added | Brad Rodgers | timeline score: 4 | |
| Oct 9, 2023 at 4:25 | comment | added | Brad Rodgers | Glad it is a useful reference! I'll repost as an answer. | |
| Oct 9, 2023 at 0:26 | comment | added | Will Sawin | @BradRodgers In fact, if you post this as an answer I will accept. | |
| Oct 7, 2023 at 18:51 | comment | added | Will Sawin | @BradRodgers This is excellent! I think with the arguments in the paper together with one additional idea I can get the $n$th cumulant as equal to some integral independent of $N$ plus $o(1)$. There's still the matter of evaluating the integral but that's actually not the most important part for me. | |
| Oct 7, 2023 at 10:12 | comment | added | Brad Rodgers | There are some papers of Soshnikov which are in this direction, though they don't answer your question as it seems like it would take some real book-keeping and maybe a new idea or two to get the calculation Keating-Snaith have for cumulants from his work. See arxiv.org/abs/math/9908063. See Lemma 2 for U(n) and (2.7) for an identity that can be applied to more general determinantal point processes. Note that $f(t) = \log(1-e^{it})$ is not in the class (1.4) he needs in this paper, but there may be some analytic ways to get around (1.4) if that restriction is the only sticking point. | |
| Oct 7, 2023 at 1:02 | history | became hot network question | |||
| Oct 6, 2023 at 17:45 | answer | added | Carlo Beenakker | timeline score: 4 | |
| Oct 6, 2023 at 16:57 | history | asked | Will Sawin | CC BY-SA 4.0 |