Ginibre ensemble
E898467
The Ginibre ensemble is a fundamental class of non-Hermitian random matrices with independently distributed complex (or real/quaternion) Gaussian entries, widely studied for its rich eigenvalue statistics in random matrix theory.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
probability distribution on matrices ⓘ random matrix ensemble ⓘ |
| contrastWith |
Gaussian Unitary Ensemble (Hermitian)
NERFINISHED
ⓘ
Hermitian Wigner ensembles ⓘ |
| eigenvalueCorrelation | determinantal point process (complex case) ⓘ |
| eigenvalueDensityLimit | uniform on unit disk after appropriate scaling ⓘ |
| eigenvalueRepulsion | present ⓘ |
| eigenvalues | generally complex ⓘ |
| eigenvalueSupport | disk of radius 1 in large-N limit (after scaling) ⓘ |
| entryMean | 0 ⓘ |
| entryVariance | 1 ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ random matrix theory ⓘ |
| hasProperty |
entries are independent but not identically distributed under some normalizations
ⓘ
non-normal matrices ⓘ rotationally invariant eigenvalue distribution in complex plane (complex case) ⓘ |
| hasVariant |
complex Ginibre ensemble
NERFINISHED
ⓘ
quaternion Ginibre ensemble NERFINISHED ⓘ real Ginibre ensemble ⓘ |
| introducedBy | Jean Ginibre NERFINISHED ⓘ |
| introducedInYear | 1965 ⓘ |
| isA | non-Hermitian random matrix ensemble ⓘ |
| matrixEntriesDistribution |
independent Gaussian entries
ⓘ
independent identically distributed complex Gaussian entries ⓘ independent identically distributed quaternion Gaussian entries ⓘ independent identically distributed real Gaussian entries ⓘ |
| namedAfter | Jean Ginibre NERFINISHED ⓘ |
| publication | Ginibre 1965 Journal of Mathematical Physics paper NERFINISHED ⓘ |
| relatedConcept |
Gaussian Orthogonal Ensemble
NERFINISHED
ⓘ
Gaussian Symplectic Ensemble NERFINISHED ⓘ Gaussian Unitary Ensemble NERFINISHED ⓘ Ginibre point process NERFINISHED ⓘ circular law ⓘ non-Hermitian spectral statistics ⓘ |
| scalingLimit | circular law for eigenvalues ⓘ |
| studiedFor |
complex eigenvalue correlations
ⓘ
eigenvalue spacing statistics ⓘ universality of non-Hermitian spectra ⓘ |
| symmetryClass | non-Hermitian ⓘ |
| typicalMatrixSize | N by N ⓘ |
| typicalNormalization | entries scaled by 1/sqrt(N) ⓘ |
| usedIn |
non-Hermitian operator theory
ⓘ
open quantum systems ⓘ quantum chaos ⓘ statistical physics ⓘ wireless communications modeling ⓘ |
Referenced by (1)
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