Timeline for An experiment on random matrices
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2017 at 16:08 | history | edited | j.c. | CC BY-SA 3.0 |
fix broken images
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| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://i583.photobucket.com/ with https://i583.photobucket.com/
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| Jul 3, 2010 at 16:02 | history | edited | j.c. | CC BY-SA 2.5 |
point out actual matrix ensemble
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| Jul 3, 2010 at 15:30 | comment | added | Helge | Actually, I think I asked for the wrong computation :-( The interesting thing would be the value for the matrix entries distributed in $[-1,1]$ and not $[\ell, 1]$ for some $\ell \in (-1,0)$. The reason for this is once one has an eigenvector with $\sum_{n=1}^{N} u(n)$ perturbation theory tells us that this gets amplified. | |
| Jul 3, 2010 at 15:04 | comment | added | Helge | @jc: Thanks. @Wadim: There are plenty of tools and recent work for random matrices. Just look at the not so few papers by Erdoes, Schlein, Tau, Vu, Yau and others.... | |
| Jul 3, 2010 at 14:45 | comment | added | Wadim Zudilin | Have you ever seen the structure of zeros of polynomials related to rational solutions of the Painlev\'e differential equations? Their structure is much more regular (and plots are nicer :-) ) but nothing is proved. | |
| Jul 3, 2010 at 14:44 | history | edited | j.c. | CC BY-SA 2.5 |
more plots
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| Jul 3, 2010 at 14:09 | comment | added | Helge | Do you mind also computing : $\max_{1\leq j \leq N} \sum_{n=1}^{N} u_j^N(n)$. Here $u_j^N$ denotes the $j$-th eigenvector of the $N \times N$ matrix. I would expect this to be $\frac{1}{2}$ based on my answer and your plots ... If this turns out to be true, one should ask oneself if this is known / proven? | |
| Jul 3, 2010 at 13:56 | comment | added | j.c. | (These plots were made in response to Helge's fine answer) | |
| Jul 3, 2010 at 13:52 | history | answered | j.c. | CC BY-SA 2.5 |