Timeline for Eigenvalue Gap Probability Through Method of Moments
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 1, 2014 at 19:26 | comment | added | ofer zeitouni | I am not sure that I understand the question, so let me answer a more general one: you can do (some) gap distributions by the method of moments if you work with non-backtracking paths, but this is not sharp in the interior of the support. See this paper of Sodin for a review: arxiv.org/abs/1406.3410 | |
| Jul 1, 2014 at 17:37 | comment | added | Carlo Beenakker | just to help me, perhaps you can be more specific what you call the "Gaudin-Metha-like" result $p(x)$? Is it the integrated spacing distribution? | |
| Jul 1, 2014 at 16:27 | comment | added | Alex R. | @CarloBeenakker: I might be mixing up terminology but, for the GUE (and therefore for the CUE), one has the Gaudin Mehta result which looks like $xe^{-cx}I(x)$ whereas for the COE there is no $x$ term out front. I've changed my wording to Gaudin-Mehta-like result just in case. | |
| Jul 1, 2014 at 16:26 | history | edited | Alex R. | CC BY-SA 3.0 |
added 3 characters in body
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| Jul 1, 2014 at 10:37 | comment | added | Carlo Beenakker | it seems to me that $1-p_n(x)$ will vanish linearly with $x$, while the Gaudin-Mehta result vanishes quadratically; the difference arises because $\lambda_1$ is not repelled from the real line; am I mistaken? (note that $M_n$ is not an orthogonal matrix, unlike the name COE suggests, it's a symmetric unitary matrix, so the real axis is not a line of symmetry) | |
| Jun 30, 2014 at 21:19 | history | asked | Alex R. | CC BY-SA 3.0 |