Timeline for Probability of complex eigenvalues
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 13, 2020 at 21:15 | comment | added | ofer zeitouni | @Ben Crowell There are $n^2$ independent random variables involved, namely the entries of the matrix... for this reason, the rate $n^2$ is typical of large deviations for the empirical measure of eigenvalues of random matrices. | |
| Aug 13, 2020 at 18:51 | comment | added | user21349 | Is there any simple heuristic that would explain why it's asymptotically an exponential in $n^c$, with $c=2$? If the probabilities were independent for the $n$ eigenvalues, we'd expect $c=1$. If every matrix element had some probability of perturbing each eigenvalue off the real line, then maybe we'd imagine $c=3$. Maybe it's like random collisions between one eigenvalue and another, where being too close causes a repulsion that forces them off the real line? That would seem to make sense of the $c=2$. | |
| Aug 13, 2020 at 15:00 | comment | added | prosti | $1-2^{- \frac{n(n-1)}{4}}$ fits nice to what I got with MC. Thanks. | |
| Aug 13, 2020 at 14:34 | vote | accept | prosti | ||
| Aug 13, 2020 at 14:06 | history | answered | Marcel | CC BY-SA 4.0 |