Journal of Stat&tical Physics, Vol. 73, Nos. 1/2, 1993. p. 253-266.
We continue the analysis of hierarchical interfaces in random media started in earlier work. We show that from the estimates on the renormalized random variables established in that work, it follows that these models possess unique Gibbs states describing mostly flat interfaces in dimension D > 3, if the disorder is weak and the temperature low enough. In the course of the proof we also present very explicit formulas for expectations of local observables.