Wigner Semicircle Law — GOE Random Matrices

Matrix size N: 50
Samples: 30
Show spacing: Regenerate

Eigenvalue density of a GOE (Gaussian Orthogonal Ensemble) random matrix converges to Wigner's semicircle ρ(λ)=√(4−λ²)/(2π) as N→∞. Level spacing P(s) follows the Wigner surmise π/2·s·exp(−πs²/4) — a hallmark of quantum chaos.