The Dyson Brownian minor process

Understand

Consider an $n\times n$ Hermitean matrix valued stochastic process $\{H_t\}_{t\geq 0}$ where the matrix elements evolve according to Ornstein-Uhlenbeck processes.

• It is well known that the eigenvalues perform a so called Dyson Brownian motion, that is they behave as Ornstein-Uhlenbeck processes conditioned never to intersect.
• In this paper we study not only the eigenvalues of the full matrix, but also the eigenvalues of all the principal minors.
• That is, the eigenvalues of the $k\times k$ in the upper left corner of $H_t$.