Random Matrix Theory

Ensemble

GOE (real symmetric) GUE (Hermitian) Wishart (positive def.) Poisson (diagonal)

Parameters

Matrix size N: 80 Samples to accumulate: 10

Statistics

Sample Now Auto Sample Clear Accumulated

Wigner's semicircle law: for N×N GOE/GUE matrices scaled by 1/√N, eigenvalue density converges to ρ(λ)=(2/π)√(1-λ²) on [-1,1] as N→∞. Level spacing p(s) follows Wigner surmise for correlated (GOE/GUE) ensembles vs Poisson e^{-s} for uncorrelated systems — a signature of quantum chaos.