Timeline for Is there any relation between moments of random matrix and its eigenvalue distribution?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2020 at 15:20 | comment | added | Michael Engelhardt | If you know the eigenvalue distribution $\rho_{A} (\lambda )$, then $\mbox{Tr} [A^m] = \int d\lambda \lambda^{m} \rho_{A} (\lambda )$. This is even true for a single matrix $A$, before averaging over an ensemble. | |
| Feb 28, 2020 at 14:28 | comment | added | Carlo Beenakker | the expectation of ${\rm tr}\, A^m$ depends only on the marginal distribution of a single eigenvalue, so it contains no information on the correlations between the eigenvalues. | |
| Feb 28, 2020 at 7:17 | comment | added | Math_Y | What is the relation between $\mathrm{Tr}[A^m]$ and eigenvalue distribution? Could you please explain with more details? | |
| Feb 28, 2020 at 7:14 | history | edited | Math_Y | CC BY-SA 4.0 |
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| Feb 28, 2020 at 0:37 | comment | added | Michael Engelhardt | If, as Yemon Choi suspects, your moments of $\mathbf{A} $ are traces of powers thereof, then you can just calculate them in the eigenbasis, where they are directly moments of the eigenvalue distribution. | |
| Feb 27, 2020 at 23:09 | comment | added | Yemon Choi | Moreover, can you specify what class of random matrices you are considering? Square? Symmetric/hermitian? etc | |
| Feb 27, 2020 at 23:07 | comment | added | Yemon Choi | I'm not familiar with the notion of a moment being matrix-valued. Are you sure you don't mean something like ${\rm Tr}((A^m)^*A^m)$? | |
| Feb 27, 2020 at 22:42 | history | edited | Math_Y | CC BY-SA 4.0 |
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| Feb 27, 2020 at 22:35 | history | asked | Math_Y | CC BY-SA 4.0 |