  Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We
discuss flat, curved, and stationary initial conditions and are interested in
the covariance of the height as a function of time at a fixed point on the
substrate. In each case the power laws of the covariance for short and long
times are obtained. They are derived from a variational problem involving two
independent Airy processes. For stationary initial conditions we derive an
exact formula for the stationary covariance with two approaches: (1) the
variational problem and (2) deriving the covariance of the time-integrated
current at the origin for the corresponding driven lattice gas. In the
stationary case we also derive the l arge time behavior for the covariance of
the height gradients.
