In mathematics, the Dyson Brownian motion is a real-valued continuous-time stochastic process named for Freeman Dyson. [1] Dyson studied this process in the context of random matrix theory.
There are several equivalent definitions: [2] [3]
Definition by stochastic differential equation:
Start with a
Hermitian matrix with eigenvalues , then let it perform Brownian motion in the space of Hermitian matrices. Its eigenvalues constitute a Dyson Brownian motion.
Start with independent Wiener processes started at different locations , then condition on those processes to be non-intersecting for all time. The resulting process is a Dyson Brownian motion starting at the same . [4]
In mathematics, the Dyson Brownian motion is a real-valued continuous-time stochastic process named for Freeman Dyson. [1] Dyson studied this process in the context of random matrix theory.
There are several equivalent definitions: [2] [3]
Definition by stochastic differential equation:
Start with a
Hermitian matrix with eigenvalues , then let it perform Brownian motion in the space of Hermitian matrices. Its eigenvalues constitute a Dyson Brownian motion.
Start with independent Wiener processes started at different locations , then condition on those processes to be non-intersecting for all time. The resulting process is a Dyson Brownian motion starting at the same . [4]