2D Coulomb Gas — Log Repulsion

Energy: 0 | Step: 0
N charges with logarithmic repulsion: E = −∑_{i≠j} log|z_i − z_j| + confinement. On a circle: equilibrium = N-th roots of unity (eigenvalues of unitary RMT). On a disk with harmonic confinement: density converges to Wigner semicircle law projected to real axis. Gradient descent with noise finds near-optimal configurations.