Timeline for Characterizations of the GOE/GUE family of distributions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2014 at 20:16 | comment | added | ofer zeitouni | Carlo's Gibbs measure+ requirement to be determinantal characterizes, I believe but have not double checked, $\beta=2$. The $\beta=1$ and $\beta=4$ can be characterized by decimation relations. | |
| Mar 11, 2014 at 19:25 | comment | added | Alex R. | That's a great question. I'm not entirely if what I'm asking for is reasonable. I've added an example below my edit which I think encapsulates what I'm after. | |
| Mar 11, 2014 at 16:32 | comment | added | Carlo Beenakker | non-random matrix characterizations: $\rho_{\beta,n}$ is the Gibbs distribution of a one-dimensional Coulomb gas in a harmonic confining potential, at temperature $1/\beta$, but that does not single out the special values $\beta=1,2,4$; any such characterization will somehow have to involve the Jacobian from matrix elements to eigenvalues, how could this arise otherwise? | |
| Mar 11, 2014 at 15:33 | comment | added | Alex R. | Thanks, the second part is particularly enlightening. I've added a slight edit to the question. Basically, is there a non-random matrix characterization of these distributions? | |
| Mar 11, 2014 at 7:40 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |