  We consider the two-point function of the totally asymmetric simple exclusion
process with stationary initial conditions. The two-point function can be
expressed as the discrete Laplacian of the variance of the associated height
function. The limit of the distribution function of the appropriately scaled
height function was obtained previously by Ferrari and Spohn. In this paper we
show that the convergence can be improved to the convergence of moments. This
implies the convergence of the two-point function in a weak sense along the
near-characteristic direction as time tends to infinity, thereby confirming the
conjecture in the paper of Ferrari and Spohn.
