The Montgomery-Odlyzko law (which is a law in the sense of empirical observation instead of through mathematical proof) states that the distribution of the spacing between successive nontrivial zeros of the Riemann zeta function (suitably normalized) is statistically identical with the distribution of eigenvalue spacings in a Gaussian unitary ensemble.

Hilbert-Pólya conjecture | Montgomery's pair correlation conjecture | Riemann zeta function zeros