Timeline for Size of Jordan blocks under random perturbations
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2016 at 21:32 | comment | added | Nick Cook | As @Mark says, the answer should be 1, but this hasn't been proved. As an application of their four moment theorem, Tao and Vu deduce a bound $O(n^{1-c})$ for some constant $c>0$ on the maximum multiplicity for a random matrix with iid entries matching the real or complex Gaussian to four moments -- see Corollary 18 here: arxiv.org/pdf/1206.1893v6.pdf. I'm not aware of any other work on eigenvalue multiplicity for non-Hermitian random matrices. | |
| Oct 20, 2016 at 13:19 | comment | added | Mark Meckes | @MarianoSuárez-Álvarez: Not necessarily. Do you believe that discrete random variables are sensible? The intuition from continuous distributions suggests that the answer to the question must be 1, but proving that for, say, a matrix with independent Bernoulli entries may be difficult. | |
| Oct 20, 2016 at 9:30 | comment | added | Daniel86 | Right, but is there a specific distribution known (with non-fixed entries mean) for which such a quantitive reault be given? From what I gathered, it is not the case. Thanks. | |
| Oct 20, 2016 at 5:24 | comment | added | user1688 | I think so too, as the set of matrices with $n$ different eigenvalues is open and dense. | |
| Oct 20, 2016 at 3:55 | comment | added | Mariano Suárez-Álvarez | Any sensible random matrix has simple eigenvalues, no? | |
| Oct 19, 2016 at 22:45 | history | asked | Daniel86 | CC BY-SA 3.0 |