Dyson Brownian Motion models random matrix eigenvalues as interacting Brownian particles with logarithmic repulsion dV = -β Σ log|λᵢ-λⱼ|. The Dyson index β=1,2,4 for GOE/GUE/GSE ensembles controls level repulsion strength. The equilibrium level spacing follows the Wigner surmise P(s) ∝ sᵝ e^(-cβs²).