Gaussian unitary ensemble
E443666
The Gaussian unitary ensemble is a fundamental random matrix ensemble of complex Hermitian matrices with statistically independent, Gaussian-distributed entries, central to quantum chaos and random matrix theory.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Gaussian Unitary Ensemble | 2 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
Gaussian ensemble
ⓘ
probability distribution ⓘ random matrix ensemble ⓘ unitary invariant ensemble ⓘ |
| alsoKnownAs | GUE NERFINISHED ⓘ |
| application |
mesoscopic physics
ⓘ
nuclear physics ⓘ number theory ⓘ quantum chaos ⓘ statistical mechanics ⓘ wireless communications ⓘ |
| belongsToClass | Wigner ensembles NERFINISHED ⓘ |
| bulkStatistics | described by sine kernel determinantal process ⓘ |
| DysonIndex | 2 ⓘ |
| edgeFluctuations | governed by Tracy–Widom GUE distribution ⓘ |
| eigenvalueCorrelation |
given by Airy kernel at soft edge
ⓘ
given by sine kernel in bulk scaling limit ⓘ |
| eigenvalueDistribution | determinantal point process ⓘ |
| eigenvalueJointDensity | proportional to exp(-Σ λ_i^2/2σ^2) Π_{i<j}(λ_i-λ_j)^2 ⓘ |
| entryDistribution | Gaussian-distributed entries ⓘ |
| entryIndependence | statistically independent entries ⓘ |
| field |
mathematical physics
ⓘ
quantum chaos ⓘ random matrix theory ⓘ |
| introducedBy | Freeman Dyson NERFINISHED ⓘ |
| invarianceProperty | invariant under conjugation by unitary matrices ⓘ |
| levelRepulsionExponent | 2 ⓘ |
| matrixType | complex Hermitian matrices ⓘ |
| parameter |
matrix size N
ⓘ
variance parameter of Gaussian entries ⓘ |
| probabilityDensityForm | proportional to exp(-Tr(H^2)/2σ^2) ⓘ |
| relatedConcept |
Airy kernel
NERFINISHED
ⓘ
Dyson Brownian motion NERFINISHED ⓘ Gaussian orthogonal ensemble NERFINISHED ⓘ Gaussian symplectic ensemble NERFINISHED ⓘ Tracy–Widom distribution NERFINISHED ⓘ Wigner semicircle law NERFINISHED ⓘ sine kernel ⓘ unitary group U(N) ⓘ |
| relatedTo | Riemann zeta function zeros (conjecturally similar statistics) ⓘ |
| symmetryClass | unitary symmetry ⓘ |
| timeReversalSymmetry | broken ⓘ |
| typicalEigenvalueDensity | Wigner semicircle distribution NERFINISHED ⓘ |
| universalityProperty | local eigenvalue statistics are universal in large N limit ⓘ |
| usedIn |
analysis of eigenvalue spacing distributions
ⓘ
study of spectral rigidity ⓘ theory of quantum transport ⓘ |
| usedToModel |
eigenvalue statistics of large complex Hermitian matrices
ⓘ
energy level statistics of quantum systems with broken time-reversal symmetry ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gaussian Unitary Ensemble
this entity surface form:
Gaussian Unitary Ensemble