Random matrix eigenvalue densities: Wigner semicircle law (GOE), Marchenko-Pastur (Wishart), and circular law (Ginibre). Watch the theoretical densities emerge from random matrix samples.
GOE: symmetric matrix H=(A+Aᵀ)/√(2N), eigenvalues follow semicircle ρ(λ)=(2/π)√(1-λ²). Wishart: W=XᵀX/N, Marchenko-Pastur law. Ginibre: complex non-symmetric — eigenvalues fill the unit disk uniformly. These laws are universal — independent of entry distribution (Tao-Vu 2012).