  In this paper, we answer a question posed by Kurt Johansson, to find a PDE
for the joint distribution of the Airy Process. The latter is a continuous
stationary process, describing the motion of the outermost particle of the
Dyson Brownian motion, when the number of particles get large, with space and
time appropriately rescaled. The question reduces to an asymptotic analysis on
the equation governing the joint probability of the eigenvalues of coupled
Gaussian Hermitian matrices. The differential equations lead to the asymptotic
behavior of the joint distribution and the correlation for the Airy process at
different times t_1 and t_2, when t_2-t_1 tends to infinity.
