Random Matrix Eigenvalue Density — Wigner Semicircle

The empirical spectral density of a large random symmetric matrix converges to the Wigner semicircle law: ρ(λ) = (2/πR²)√(R²−λ²), independent of the entry distribution (universality).

Parameters

Matrix size N 80 Entry distribution Number of samples 5

ρ(λ) = (2/πR²)√(R²−λ²)
R = 2σ√N (Wigner radius)
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