Random Matrix Theory — GUE Eigenvalue Density
Wigner semicircle law: ρ(λ) = √(4−λ²)/(2π), level repulsion P(s) ~ s²
Parameters
Matrix size N:
60
Ensemble:
GUE (complex Hermitian)
GOE (real symmetric)
Wishart / Marchenko-Pastur
Samples:
1
Sample New Matrix
Auto-sample
GUE: H = (A+A†)/√(2N), A_{ij}~CN(0,1)
Semicircle: ρ(λ) = √(4−λ²)/(2π)
Support: [−2, +2]
GOE spacing: P(s) ~ s·e^(−πs²/4)
GUE spacing: P(s) ~ s²·e^(−4s²/π)
Wigner-Dyson: level repulsion β=1,2,4
Ensemble size:
—
Mean λ:
—
Spectral radius:
—
Auto:
off