Timeline for Riemann-Hilbert approach to Selberg integral
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| S Jan 13, 2022 at 15:51 | history | bounty ended | Marcel | ||
| S Jan 13, 2022 at 15:51 | history | notice removed | Marcel | ||
| Jan 10, 2022 at 18:35 | vote | accept | Marcel | ||
| Jan 7, 2022 at 11:49 | history | edited | YCor |
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| Jan 7, 2022 at 11:20 | answer | added | Carlo Beenakker | timeline score: 5 | |
| S Jan 6, 2022 at 15:01 | history | bounty started | Marcel | ||
| S Jan 6, 2022 at 15:01 | history | notice added | Marcel | Draw attention | |
| Jan 6, 2022 at 12:55 | comment | added | Marcel | @dan_fulea that potential is of interest as a test ground precisely because it leads to a Selberg integral, which is exactly solvable. | |
| Jan 6, 2022 at 12:35 | comment | added | Marcel | @dan_fulea $X$ is diagonal, I have included that. The question is in fact whether the first integral is amenable to R-H, so I removed the "have seen" comment as it was confusing. The second formula for the integral is due to Selberg, this is a classical result. I have no idea how to use R-H in small dimensions (in fact I suspect it is designed to be used in large $N$ situations but I am not sure). | |
| Jan 6, 2022 at 12:31 | history | edited | Marcel | CC BY-SA 4.0 |
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| Jan 6, 2022 at 11:46 | comment | added | dan_fulea | Please give more details and/or references for the question. For instance: $X$ of shape $N$ in the "interval" from zero to infinity means $X$ is in which ensamble more exactly? From what can be seen where the integral defining $f(a,N)$ is amenable to the R-H approach? How to get the second formula for $f(a,N)$ (alternatively)? How can the R-H approach be used to produce the Selberg result in small dimensions, e.g. $N=1$ (and $N=2$)? And why is the "potential" $$V(M) = \sum_{k\ge 1} \frac 1k M^k$$of interest? | |
| Jan 5, 2022 at 12:24 | history | edited | Marcel | CC BY-SA 4.0 |
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| Jan 4, 2022 at 21:38 | comment | added | Shannon Starr | ``in which case it gives $-\log(\det(I-X))$ so ...'' | |
| Jan 4, 2022 at 18:05 | review | Suggested edits | |||
| Jan 4, 2022 at 18:09 | |||||
| Jan 4, 2022 at 14:57 | history | asked | Marcel | CC BY-SA 4.0 |