Equilibrium Fluctuations for a One-Dimensional Interface in the Solid on Solid Approximation

An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no a priori restrictions on the discret e gradient of the interface. The interaction Hamiltonian of the interface is given by a finite range part, pr oportional to the sum of height differences, plus a part of exponentially decaying long range potentials. The evolution of the interface is a reversible Markov process. We prove that if this system is started in the center of a box of size L after a time of order L^3 it reaches, with a very large probability, the top or the bottom of the box.