3 problems

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Dyson's bulk GUE gap probability asymptotic conjecture
Let $P(s)$ be the probability that there are no bulk GUE eigenvalues in the interval $\left(-\frac{s}{\pi},\frac{s}{\pi}\right)$ , and let $c_0$ be a constant. Dyson's conjecture. A…
Conjectureopengap-probabilities gue random-matrix-theoryarXiv posted 2 days ago
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Existence of the limiting GUE level-crossing density
For each $n$ , let $\mathcal P_n^{GUE}(\theta,\phi)$ denote the level-crossing density for a pencil of independent GUE matrices, expressed in spherical coordinates $(\theta,\phi)$ o…
Conjectureopengue level-crossings random-matricesarXiv posted 2 days ago
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The sharp lower-envelope conjecture for GUE minor-process extremal eigenvalues
Lower-envelope conjecture.
Conjectureopeneigenvalue-fluctuations gue random-matricesarXiv posted 2 days ago

Dyson's bulk GUE gap probability asymptotic conjecture