Paper replications#
Classic random matrix theory results, organized around Dyson’s threefold way and its non-Hermitian/chiral/Bogoliubov-de Gennes extensions: Wishart’s original sample-covariance construction, the Wigner semicircle and surmise, the Marchenko-Pastur and Wachter laws, the Tracy-Widom edge distributions, Dyson’s circular ensembles and the Keating-Snaith characteristic-polynomial moments, spectral rigidity and universality, the Pandey-Mehta GOE-GUE crossover, the Poisson (Berry-Tabor) integrable baseline, Ginibre’s circular law, the single ring theorem, PT-symmetry breaking, Anderson localization, the Altland-Zirnbauer Bogoliubov-de Gennes symmetry classes, the Two-Body Random Ensemble, Page’s average-entanglement-entropy conjecture, the Dumitriu-Edelman tridiagonal model, and Kitaev’s SYK model.
Altland-Zirnbauer Classes: BdG Eigenvalue Symmetry
The Two-Body Random Ensemble: Gaussian, not Semicircle
Keating-Snaith Moments of the CUE Characteristic Polynomial
Anderson Localization in Power-Law Banded Matrices
Page’s Conjecture: the Average Entanglement Entropy of a Random State
PT-Symmetry Breaking in Pseudo-Hermitian Ensembles
Kitaev’s SYK Model: Majorana Fermions, Wigner-Dyson Statistics
