Timeline for Singular values of sparse random real-valued matrix
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 24, 2019 at 7:54 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Dec 19, 2016 at 16:23 | vote | accept | user19346 | ||
| Dec 19, 2016 at 7:16 | comment | added | Carlo Beenakker | there is a closed form solution for the binary distribution in the 2006 paper (the "effective medium" theory); it is given on pages 14 and 15, involves solving a cubic equation; more generally, for the Gaussian distribution, you would need to solve a transcendental equation, which can only be done numerically; all of this is in the limit $N\rightarrow\infty$ for fixed $\alpha,p$, in which Marchenko-Pastur does not hold. | |
| Dec 18, 2016 at 23:20 | comment | added | user19346 | Thanks for your answer! For the 2008 paper, is there a way to even get a closed form for the spectral density of a matrix with nonzero elements that are from -1 and +1 with equal probability, when c is small? Or can this only be done numerically with their methods? They recover Marchenko-Pastur in (30) when c is large, and I'm interested if an analytic form can be derived using (26) and (27) when c is small. | |
| Dec 18, 2016 at 13:52 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |