GUE eigenvalue density (Wigner semicircle) + largest eigenvalue (Tracy-Widom)
Parameters
Eigenvalues—
λ_max mean—
λ_max std—
Semicircle R—
Wigner semicircle law: For GUE(N), bulk eigenvalue density → ρ(λ)=(1/2πσ²)√(4σ²−λ²).
Tracy-Widom: Largest eigenvalue λ_max fluctuates on scale N⁻²/³ with TW₂ distribution — universal at the spectral edge, appears in random growth models (KPZ universality class).