Gaussian unitary ensemble

URI: https://gptkb.org/entity/Gaussian_unitary_ensemble
GPTKB entity
Statements (27)
Predicate Object
gptkbp:instanceOf random matrix ensemble
gptkbp:abbreviation gptkb:GUE
gptkbp:application number theory
statistical physics
quantum chaos
gptkbp:eigenvalue_distribution joint probability density function
gptkbp:eigenvalue_statistics universal in large N limit
gptkbp:ensemble_average over Hermitian matrices
gptkbp:field gptkb:mathematics
mathematical physics
random matrix theory
gptkbp:hasInvariant unitary transformations
https://www.w3.org/2000/01/rdf-schema#label Gaussian unitary ensemble
gptkbp:introduced gptkb:Eugene_Wigner
gptkbp:matrix_entries complex numbers
gptkbp:matrix_entries_distribution gptkb:Gaussian_distribution
gptkbp:matrix_size N x N
gptkbp:matrix_type gptkb:Hermitian_matrices
gptkbp:probability_measure proportional to exp(-Tr(H^2))
gptkbp:relatedTo gptkb:Wigner_semicircle_law
gptkb:Gaussian_orthogonal_ensemble
gptkb:Gaussian_symplectic_ensemble
Dyson index β=2
gptkbp:symmetry_class unitary symmetry
gptkbp:used_in study of spectral statistics
gptkbp:bfsParent gptkb:Wigner_surmise
gptkbp:bfsLayer 5