Eigenvalue Repulsion — Random Matrix GOE

GOE/GUE/GSE random matrices · level spacing P(s)

Ensemble β

Matrix size N: 150

Samples: 40

Wigner surmise: P(s) = A_β s^β exp(−B_β s²) for β=1,2,4.
Level repulsion exponent β: 1=GOE (time-reversal), 2=GUE (broken TR), 4=GSE (spin-½ TR).
Poisson: P(s)=e^−s — no repulsion, levels can cluster.