GUE/GOE eigenvalue spacing — level repulsion and Wigner surmise
Eigenvalue Distribution
Level Spacing P(s)
GUE: P(s) ≈ (32/π²)s²e^(−4s²/π) — Wigner surmise. Level repulsion: P(s)~sᵝ near s=0. Semicircle law: ρ(λ)=(1/2π)√(4−λ²).