  We study a symmetric randomly moving line interacting by exclusion with a
wall. We show that the expectation of the position of the line at the origin
when it starts attached to the wall satisfies the following bounds: c_1t^{1/4}
\le\E\xi_t(0) \le c_2 t^{1/4}\log t The result is obtained by comparison with a
``free'' process, a random line that has the same behavior but does not see the
wall. The free process is isomorphic to the symmetric nearest neigbor
one-dimensional simple exclusion process. The height at the origin in the
interface model corresponds to the integrated flux of particles through the
origin in the simple exclusion process. We compute explicitly the asymptotic
variance of the flux and show that the probability that this flux exceeds
Kt^{1/4}\log t is bounded above by const. t^{2-K}. We have also performed
numerical simulations, which indicate \E\xi_t(0)^2 \sim t^{1/2}\log t as
t\to\infty.
