random matrix theory
E259756
Random matrix theory is a branch of mathematics and mathematical physics that studies the statistical properties of matrices with randomly chosen entries, with deep applications to fields such as number theory, quantum chaos, and statistical mechanics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| random matrix theory canonical | 1 |
Statements (69)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematical physics
ⓘ
branch of mathematics ⓘ |
| appliesTo |
compressed sensing
ⓘ
finance ⓘ machine learning ⓘ multivariate statistics ⓘ nuclear physics ⓘ number theory ⓘ quantum chaos ⓘ statistical mechanics ⓘ wireless communications ⓘ |
| developedBy |
Eugene Wigner
ⓘ
Freeman Dyson ⓘ Leonid Pastur ⓘ Madame Tracy and Widom (Craig Tracy and Harold Widom) ⓘ Marcin Kac ⓘ Vladimir Marchenko ⓘ |
| emergedIn | 1950s ⓘ |
| fieldOfStudy | random matrices ⓘ |
| hasApplicationType |
modeling complex quantum systems
ⓘ
modeling energy level statistics ⓘ modeling high-dimensional data ⓘ |
| hasKeyConcept |
BBP phase transition
ⓘ
Dyson Brownian motion ⓘ Gaussian orthogonal ensemble ⓘ
surface form:
Gaussian Orthogonal Ensemble
Gaussian symplectic ensemble ⓘ
surface form:
Gaussian Symplectic Ensemble
Gaussian unitary ensemble ⓘ
surface form:
Gaussian Unitary Ensemble
Ginibre ensemble ⓘ Marchenko–Pastur law ⓘ Stieltjes transform ⓘ Tracy–Widom distribution ⓘ Wigner matrices ⓘ Wigner semicircle law ⓘ Wishart distribution ⓘ
surface form:
Wishart matrices
beta-ensembles ⓘ circular law ⓘ concentration of measure ⓘ delocalization of eigenvectors ⓘ determinantal point processes ⓘ eigenvalue rigidity ⓘ free probability ⓘ global spectral statistics ⓘ isotropic local laws ⓘ large deviations for eigenvalues ⓘ level repulsion ⓘ local semicircle law ⓘ local spectral statistics ⓘ non-Hermitian random matrices ⓘ orthogonal polynomial ensembles ⓘ random band matrices ⓘ resolvent method ⓘ sample covariance matrices ⓘ sparse random matrices ⓘ spiked models ⓘ universality ⓘ |
| originatedIn | nuclear physics ⓘ |
| relatedTo |
GUE hypothesis for zeta zeros
ⓘ
Montgomery's pair correlation conjecture ⓘ
surface form:
Montgomery pair correlation conjecture
Riemann zeta function ⓘ
surface form:
Riemann zeta function zeros
quantum chaos conjectures ⓘ |
| studies |
eigenvalue distributions of random matrices
ⓘ
eigenvector statistics of random matrices ⓘ spectral statistics ⓘ statistical properties of matrices with random entries ⓘ |
| usedIn |
MIMO communication theory
ⓘ
high-dimensional statistics ⓘ mesoscopic physics ⓘ PCA ⓘ
surface form:
principal component analysis
quantum transport ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.