Examples#

Paper-replication scripts for physicskit.rmt, organized around Dyson’s threefold way: each script reproduces a classic random matrix theory result to numerical precision against its published closed-form law or reference.

Every script is real Python you can run directly (python examples/rmt/paper_replications/<script>.py) and is also executed live at documentation-build time to produce the gallery pages below – the script is the source of truth for what you see, not a copy of it.

Replications#

Wigner-Dyson statistics – Wigner’s semicircle law for the bulk spectral density, the Wigner surmise for nearest-neighbor level spacing, Tracy-Widom soft-edge laws, spectral rigidity and universality, the Pandey-Mehta GOE-GUE crossover, and the Poisson (Berry-Tabor) baseline for integrable, non-chaotic spectra.
Beyond GOE/GUE/GSE – Dyson’s circular ensembles (COE, CUE, CSE) and the Keating-Snaith moments of the CUE characteristic polynomial, the Marchenko-Pastur law for Wishart covariance matrices (and Wishart’s original finite-sample data-matrix construction), the Wachter law for Jacobi ensembles, and Ginibre’s circular law for non-Hermitian matrices.
Symmetry classes, disorder, and non-Hermiticity – the Altland-Zirnbauer superconductor classes’ Bogoliubov-de Gennes eigenvalue symmetry, the Anderson localization transition in power-law banded matrices, and PT-symmetry breaking in pseudo-Hermitian ensembles.
Many-body and computational random matrix theory – the Two-Body Random Ensemble’s Gaussian (not semicircular) many-body density of states, Kitaev’s SYK model and its Wigner-Dyson many-body level statistics, Page’s conjecture for the average entanglement entropy of a random quantum state, and the Dumitriu-Edelman tridiagonal model that makes continuum-beta simulation possible at all.

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.