Spacings and spectral correlations#
Level repulsion and its consequences: the Wigner surmise, Dyson’s circular ensembles and the sine kernel, the Keating-Snaith moments of the CUE characteristic polynomial, the Poisson (Berry-Tabor) integrable baseline, the Pandey-Mehta GOE-GUE crossover, Bohigas-Giannoni-Schmit spectral rigidity and universality, and the Wigner-Dyson many-body level statistics of Kitaev’s SYK model.
The Berry-Tabor Conjecture: Poisson Statistics for Integrable Spectra
The Berry-Tabor Conjecture: Poisson Statistics for Integrable Spectra
The Bohigas-Giannoni-Schmit Conjecture: Spectral Rigidity and Universality
The Bohigas-Giannoni-Schmit Conjecture: Spectral Rigidity and Universality
Dyson’s Threefold Way: the Circular Ensembles COE, CUE, CSE
Dyson's Threefold Way: the Circular Ensembles COE, CUE, CSE
Kitaev’s SYK Model: Majorana Fermions, Wigner-Dyson Statistics
Kitaev's SYK Model: Majorana Fermions, Wigner-Dyson Statistics
The Riemann Zeta Connection: Keating-Snaith Moments of the CUE Characteristic Polynomial
The Riemann Zeta Connection: Keating-Snaith Moments of the CUE Characteristic Polynomial
