Circular Unitary Ensemble (CUE)
Random unitary matrices — eigenvalue repulsion on the unit circle
Parameters
Matrix size N:
50
Samples:
500
Histogram bins:
40
Generate New Sample
Accumulate (10x)
Total eigenvalues:
0
Mean spacing:
0
Ensemble:
CUE (β=2)
CUE: β=2 (complex). Eigenvalues of Haar-random U(N) lie on the unit circle.
Level spacing follows
Wigner surmise
: p(s) = (32/π²)s²exp(−4s²/π)
Key feature: eigenvalue
repulsion
— no clustering, unlike Poisson (no interactions → exp distribution).