GOE
Eigenvalue Repulsion
Level repulsion in the Gaussian Orthogonal Ensemble — Wigner surmise vs Poisson statistics
Matrix size N
80
Samples
100
Ensemble type
GOE (real symmetric)
GUE (complex Hermitian)
Poisson (integrable)
Resample & Compute
Nearest-Neighbor Spacing Distribution p(s)
Empirical histogram
Wigner surmise GOE
Poisson
Eigenvalue Positions on Number Line
—
Mean spacing
—
Variance
—
r-statistic