  Putting dynamics into random matrix models leads to finitely many
nonintersecting Brownian motions on the real line for the eigenvalues, as was
discovered by Dyson. Applying scaling limits to the random matrix models,
combined with Dyson's dynamics, then leads to interesting, infinite-dimensional
diffusions for the eigenvalues. This paper studies the relationship between two
of the models, namely the Airy and Pearcey processes and more precisely shows
how to approximate the multi-time statistics for the Pearcey process by the one
of the Airy process with the help of a PDE governing the gap probabilities for
the Pearcey process.
