Coram–Diaconis self-similarity conjecture for CUE eigenvalues
Let UUU be an N×NN\times NN×N random matrix from the circular unitary ensemble with eigenvalues {eiθj}1≤j≤N\{e^{i\theta_j}\}_{1\le j\le N}{eiθj}1≤j≤N, where 0≤θ1≤⋯≤θN<2π0\le \theta_1\le\dots\le\theta_N<2\pi0≤θ1≤⋯≤θN<2π. Choose…