  We study the spatial correlations of the one-dimensional KPZ surface for the
flat initial condition. It is shown that the multi-point joint distribution for
the height is given by a Fredholm determinant, with its kernel in the scaling
limit explicitly obtained. This may also describe the dynamics of the largest
eigenvalue in the GOE Dyson's Brownian motion model. Our analysis is based on a
reformulation of the determinantal Green's function for the totally ASEP in
terms of a vicious walk problem.
