For the SYK model with even q much smaller than sqrt(N), local eigenvalue statistics match a Gaussian law down to scales q/sqrt(N), and eigenvectors delocalize in any deterministic basis.
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Weak local law and delocalization for the Sachdev-Ye-Kitaev model
For the SYK model with even q much smaller than sqrt(N), local eigenvalue statistics match a Gaussian law down to scales q/sqrt(N), and eigenvectors delocalize in any deterministic basis.