A dynamic one-dimensional interface interacting with a wall

Abstract

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\Eξ_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 \Eξ_t(0)^2 \sim t^{1/2}\log t as t\to\infty.