RANDOM MATRIX EIGENVALUES

GUE · GOE · Poisson · Wigner surmise

Matrix size N = 100 Samples = 50

-Mean spacing

-Variance

-Matrix size

-Eigenvalues

GUE (β=2): level repulsion P(s) ~ s²·e^(-πs²/4) — Wigner surmise. GOE (β=1): P(s) ~ s·e^(-πs²/4). Poisson: P(s) = e^(-s) — no repulsion. The Riemann zeros are conjectured to follow GUE statistics.