Tracy–Widom distribution
E898464
The Tracy–Widom distribution is a probability distribution that describes the fluctuations of the largest eigenvalue in many classes of large random matrices and appears widely in random matrix theory and related probabilistic limit theorems.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
distribution in random matrix theory
ⓘ
limiting distribution ⓘ probability distribution ⓘ |
| appearsIn |
combinatorial probability
ⓘ
growth models in the KPZ universality class ⓘ last passage percolation ⓘ longest increasing subsequence of random permutations ⓘ non-intersecting random walks ⓘ statistics of extreme eigenvalues ⓘ |
| arisesIn |
Gaussian orthogonal ensemble
NERFINISHED
ⓘ
Gaussian symplectic ensemble NERFINISHED ⓘ Gaussian unitary ensemble NERFINISHED ⓘ |
| belongsTo | universality class of edge eigenvalue fluctuations ⓘ |
| definedVia |
Fredholm determinant of the Airy kernel
ⓘ
solution of a Painlevé II differential equation ⓘ |
| describes | fluctuations of the largest eigenvalue of large random matrices ⓘ |
| field |
probability theory
ⓘ
random matrix theory ⓘ |
| generalizes | classical extreme value distributions for eigenvalues ⓘ |
| governs | edge scaling limit of eigenvalues ⓘ |
| hasAbbreviation | TW distribution NERFINISHED ⓘ |
| hasKurtosisExcess | approximately 0.16524294 for type II ⓘ |
| hasMean | approximately -1.2065335745820 for type II ⓘ |
| hasSkewness | approximately 0.293464524 for type II ⓘ |
| hasVariance | approximately 1.607781034581 for type II ⓘ |
| hasVariant |
Tracy–Widom distribution of type I
NERFINISHED
ⓘ
Tracy–Widom distribution of type II NERFINISHED ⓘ Tracy–Widom distribution of type III ⓘ |
| introducedBy |
Craig Tracy
NERFINISHED
ⓘ
Harold Widom NERFINISHED ⓘ |
| introducedIn | 1990s ⓘ |
| namedAfter |
Craig Tracy
NERFINISHED
ⓘ
Harold Widom NERFINISHED ⓘ |
| parameterizes | edge fluctuations of eigenvalues ⓘ |
| relatedTo |
Airy kernel
NERFINISHED
ⓘ
Gaussian ensembles NERFINISHED ⓘ Painlevé II equation NERFINISHED ⓘ Wigner matrices ⓘ Wishart matrices NERFINISHED ⓘ |
| support | subset of the real line ⓘ |
| tailBehavior |
asymmetric
ⓘ
stretched exponential decay ⓘ |
| usedFor | asymptotic distribution of the largest eigenvalue ⓘ |
| usedIn |
high-dimensional statistics
ⓘ
multivariate statistical testing ⓘ principal component analysis asymptotics ⓘ signal detection in noise ⓘ wireless communications theory ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.