Timeline for Mehta integral and orthogonality
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2020 at 20:49 | history | bounty ended | Sascha | ||
| Feb 16, 2020 at 15:30 | comment | added | Carlo Beenakker | yes, this somehow makes sense if you think of case 2 approaching case 3 when $\alpha\rightarrow\infty$ (hence $\nu\rightarrow 1/\sqrt 2$), and approaching case 1 if $\alpha\rightarrow 0$ (hence $\nu\rightarrow 0$). | |
| Feb 16, 2020 at 15:16 | comment | added | Pritam Bemis | very interesting, so in Case 3: we do not see $\gamma$ at all in the limit and in this regime $2$, although the value is of order $1$, it vanishes as $\alpha$ tends to zero. | |
| Feb 16, 2020 at 15:15 | vote | accept | Pritam Bemis | ||
| Feb 16, 2020 at 13:47 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 16, 2020 at 13:34 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 16, 2020 at 12:51 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 16, 2020 at 12:44 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 16, 2020 at 12:36 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 16, 2020 at 12:29 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 16, 2020 at 12:17 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 15, 2020 at 15:48 | comment | added | Pritam Bemis | thank you for your prompt response. This sounds very plausible. I will update the question accordingly. | |
| Feb 15, 2020 at 15:35 | comment | added | Carlo Beenakker | my "conjecture" would be to substitute $\gamma n=\text{constant}$ in the formula for $\nu$, which would give $\nu=0$ in case 2; incidentally, the plots you show do not take into account the repulsion between the $x_i$'s with $i$ unequal to 1, so I don't think one can draw any conclusion from those. | |
| Feb 15, 2020 at 15:13 | comment | added | Pritam Bemis | thank you, that's interesting. Do you have any conjectures about case 2 whether the result will be of "order 1" or "tend to zero"? | |
| Feb 15, 2020 at 14:40 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Feb 15, 2020 at 14:35 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |