Wigner semicircle:
ρ(x) = (2/πR²)√(R²-x²)
R = 2√N (radius)
Level repulsion:
p(s) ∝ s^β · e^{-c·s²}
β=1 (GOE), 2 (GUE), 4 (GSE)
Universality: spacing statistics depend only on β, not the specific distribution of entries
Connection: GUE eigenvalues ≡ eigenvalues of Laplacian on arithmetic surfaces (Montgomery-Odlyzko for Riemann zeros)