Timeline for On the numerical range of non-self adjoint Gaussian matrix
Current License: CC BY-SA 3.0
6 events
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| May 7, 2016 at 1:46 | comment | added | gondolf | Thank you! Can you provide some references? I would like to have the exact dependence of the probability and $\epsilon$. | |
| May 6, 2016 at 12:40 | comment | added | Mikael de la Salle | You probably know that the numerical range is convex, so typically 0 belongs to it. So $r=0$ with probability going to $1$ (and probably with probability $\geg 1-e^{-cn^2} $). If you want more precise information, my guess is that the probability that $r>c$ behaves as $e^{-I (c) n^2}$ for some function I. Look at large deviations for random matrices. | |
| May 6, 2016 at 11:03 | history | edited | gondolf | CC BY-SA 3.0 |
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| May 6, 2016 at 10:12 | comment | added | Liviu Nicolaescu | I guess you need to be more specific about what you mean by Gaussian matrix. There are are $n^4$ degrees of freedom in choosing a Gaussian probability measure on the vector space of $n\times n$ complex matrices. | |
| May 6, 2016 at 1:54 | history | edited | gondolf | CC BY-SA 3.0 |
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| May 6, 2016 at 1:06 | history | asked | gondolf | CC BY-SA 3.0 |