  We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the
strong-coupling regime, focusing on the long time properties. By a saddle point
analysis of the mode-coupling equations, we derive exact results for the
correlation function in the long time limit - a limit which is hard to study
using simulations. The correlation function at wavevector k in dimension d is
found to behave asymptotically at time t as C(k,t)\simeq 1/k^{d+4-2z}
(Btk^z)^{\gamma/z} e^{-(Btk^z)^{1/z}}, with \gamma=(d-1)/2, A a determined
constant and B a scale factor.
