Timeline for Deterministic matrices with random matrix properties
Current License: CC BY-SA 4.0
6 events
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| Aug 22, 2020 at 13:20 | comment | added | ofer zeitouni | en.wikipedia.org/wiki/Wigner_surmise describes Wigner's surmise. The law there is not the one you get from the sine process (see Mehta), but is close numerically. About your question, I suspect you can cook it up by modifying, in the Jacobi construction, the the off-diagonal entries in a periodic way (scale $\sqrt{1/k}$), but I have not done the computation. | |
| Aug 22, 2020 at 13:05 | comment | added | Curt von Keyserlingk | Thanks! Could you provide a reference explaining why Wigner surmise is not precisely the distribution of spacings? Supposing I replace my requirement for wigner surmise with the requirement that level correlations exhibit sine kernel behaviour in the appropriate scaling limit. Is there then an answer to my question? | |
| Aug 22, 2020 at 12:16 | comment | added | ofer zeitouni | Lets not argue about what you asked originally. Wigner surmise is not the true distribution of spacings, in a precise mathematical sense, so if you go in the direction of spacings, you should be a bit more explicit as to what you look for. Are you trying to get the sine process? Let me mention also, following Suvrit, that for the function field case, the relation between the zeros of zeta function and RMT is a theorem, due to Katz-Sarnak. | |
| Aug 22, 2020 at 8:33 | comment | added | Curt von Keyserlingk | I did ask about the level spacing distribution! (I've updated the question to make this clearer). Is there an an example for that case? But thank you for this partial answer. | |
| Aug 21, 2020 at 23:19 | history | edited | ofer zeitouni | CC BY-SA 4.0 |
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| Aug 21, 2020 at 22:33 | history | answered | ofer zeitouni | CC BY-SA 4.0 |