Timeline for Eigenvalue distribution of random matrices
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2022 at 1:03 | comment | added | gondolf | @zeitouni Thank you very much!!! Are another basis well studied rather than the standard basis? | |
| Aug 20, 2022 at 20:46 | comment | added | ofer zeitouni | If your $M_i$ are the standard basis (that is $M_{\alpha \beta}$ is the matrix all of whose entries are 0 except for the $(\alpha \beta)$ entry which equals $1$) and $x_i$ are Gaussian then your matrix is a real Ginibre one, and the joint distribution of its singular values (modulu permutation) corresponds to Wishart. The limiting empirical measure is then the Marchenko-Pastur law, and the sum of singular values is expressible as its mean. | |
| Aug 15, 2022 at 9:04 | history | edited | YCor |
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| Aug 14, 2022 at 23:38 | comment | added | gondolf | @Stanley Yes. Thank you very much for clarifying this point. I think I am more interested in the distribution of the sum of singular values. | |
| Aug 14, 2022 at 23:36 | history | edited | gondolf | CC BY-SA 4.0 |
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| Aug 14, 2022 at 2:43 | comment | added | Richard Stanley | If you want to map a $d\times d$ complex matrix $M$ to a vector $v$ in $\mathbb{C}^d$ that records the eigenvalues of $M$, then we should take $v=(e_1,\dots,e_d)$, where $e_i$ is the $i$th elementary symmetric function of the eigenvalues. | |
| Aug 13, 2022 at 15:24 | comment | added | Richard Stanley | In what order do you put the eigenvalues in the vector? | |
| Aug 13, 2022 at 11:23 | comment | added | gondolf | I am interested in the vector of eigenvalues. | |
| Aug 13, 2022 at 3:05 | comment | added | Richard Stanley | Do you mean multiset rather than vector of eigenvalues? | |
| Aug 13, 2022 at 1:57 | history | edited | gondolf | CC BY-SA 4.0 |
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| Aug 12, 2022 at 22:57 | history | edited | LSpice | CC BY-SA 4.0 |
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| Aug 12, 2022 at 22:18 | history | edited | gondolf | CC BY-SA 4.0 |
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| Aug 12, 2022 at 22:13 | history | asked | gondolf | CC BY-SA 4.0 |