  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 $H_t$. If you project this process to a
space-like path it is a determinantal process and we compute the kernel. This
kernel contains as special cases the well known GUE minor kernel, discovered by
Johansson-Nordenstam and Okounkov-Reshetikhin in 2006, and the Dyson Brownian
motion kernel discovered by Forrester-Nagao in 1998.
  In the bulk scaling limit of this kernel it is possible to recover a
time-dependent generalisation of Boutillier's bead kernel.
