Spectral Statistics — Wigner–Dyson Distribution

Random matrix theory predicts universal nearest-neighbor level-spacing distributions. GOE (β=1): p(s) = (π/2)s exp(−πs²/4). GUE (β=2): p(s) = (32/π²)s² exp(−4s²/π). Poisson (integrable systems): p(s) = e^(−s). Wigner surmise is exact for 2×2 matrices.