  We analyze the mixing time of a natural local Markov chain (the Glauber
dynamics) on configurations of the solid-on-solid model of statistical physics.
This model has been proposed, among other things, as an idealization of the
behavior of contours in the Ising model at low temperatures. Our main result is
an upper bound on the mixing time of $O~(n^{3.5})$, which is tight within a
factor of $O~(sqrt{n})$. (The notation O~ hides factors that are logarithmic in
n.) The proof, which in addition gives some insight into the actual evolution
of the contours, requires the introduction of a number of novel analytical
techniques that we conjecture will have other applications.
