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]
^Bouchaud, Jean-Philippe; Potters, Marc, eds. (2020), "Dyson Brownian Motion", A First Course in Random Matrix Theory: for Physicists, Engineers and Data Scientists, Cambridge: Cambridge University Press, pp. 121–135, ISBN978-1-108-48808-2, retrieved 2023-11-25