Eigenvalue Repulsion — Random Matrix Theory

GUE/GOE level spacing statistics. Eigenvalues of random matrices repel each other — unlike independent (Poisson) levels.

Ensemble
Matrix size N = 80
Samples = 300
Wigner surmise: GOE → p(s)≈(π/2)s·exp(−πs²/4), GUE → p(s)≈(32/π²)s²·exp(−4s²/π). Poisson → p(s)=exp(−s). The "level repulsion" exponent β=1 (GOE), 2 (GUE), 4 (GSE) reflects time-reversal symmetry.