  We determine the stationary two-point correlation function of the
one-dimensional KPZ equation through the scaling limit of a solvable
microscopic model, the polynuclear growth model. The equivalence to a directed
polymer problem with specific boundary conditions allows one to express the
corresponding scaling function in terms of the solution to a Riemann-Hilbert
problem related to the Painleve II equation. We solve these equations
numerically with very high precision and compare our, up to numerical rounding
exact, result with the prediction of Colaiori and Moore [1] obtained from the
mode coupling approximation.

Statistical Mechanics