Dyson Brownian motion
E898465
Dyson Brownian motion is a stochastic process describing the time evolution of eigenvalues of random matrices as if they were interacting particles undergoing Brownian motion, fundamental in random matrix theory.
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
model in random matrix theory
ⓘ
stochastic process ⓘ |
| appliesTo |
Hermitian matrices
ⓘ
symmetric matrices ⓘ unitary invariant ensembles ⓘ |
| basedOn | Brownian motion NERFINISHED ⓘ |
| connectedTo |
beta-Jacobi ensembles
NERFINISHED
ⓘ
beta-Laguerre ensembles ⓘ |
| correspondsTo | beta-ensembles in random matrix theory ⓘ |
| describes |
interacting particle system
ⓘ
time evolution of eigenvalues of random matrices ⓘ |
| feature |
eigenvalue repulsion at short distances
ⓘ
logarithmic pairwise interaction potential ⓘ |
| field |
mathematical physics
ⓘ
probability theory ⓘ random matrix theory ⓘ |
| governs | joint distribution of eigenvalues over time ⓘ |
| hasContinuousTimeParameter | time GENERATED ⓘ |
| hasParameter | inverse temperature beta ⓘ |
| hasProperty |
Markov property
ⓘ
stationary distribution equal to invariant ensemble ⓘ |
| hasSpecialCase |
Gaussian Orthogonal Ensemble eigenvalue process
NERFINISHED
ⓘ
Gaussian Symplectic Ensemble eigenvalue process NERFINISHED ⓘ Gaussian Unitary Ensemble eigenvalue process NERFINISHED ⓘ |
| hasStateSpace | ordered eigenvalue configurations ⓘ |
| influenced |
development of beta-ensembles
ⓘ
modern universality proofs in random matrix theory ⓘ |
| introducedBy | Freeman Dyson NERFINISHED ⓘ |
| limit | equilibrium distribution given by classical random matrix ensembles ⓘ |
| models |
eigenvalue dynamics of Hermitian random matrices
ⓘ
repulsion between eigenvalues ⓘ |
| namedAfter | Freeman Dyson NERFINISHED ⓘ |
| relatedTo |
Coulomb gas model
NERFINISHED
ⓘ
Ornstein–Uhlenbeck process on matrices NERFINISHED ⓘ log-gas ensembles ⓘ |
| satisfies | system of coupled stochastic differential equations ⓘ |
| usedFor |
deriving local eigenvalue statistics
ⓘ
studying relaxation to equilibrium of eigenvalues ⓘ |
| usedIn |
connections with integrable systems
ⓘ
proofs of convergence to Wigner semicircle law ⓘ study of spectral statistics of large random matrices ⓘ universality results in random matrix theory ⓘ |
| yearIntroduced | 1962 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.