Stabilization by rough noise for an epitaxial growth model

Abstract

In this article we study a model from epitaxial thin-film growth. It was originally introduced as a phenomenological model of growth in the presence of a Schwoebbel barrier, where diffusing particles on a terrace are not allowed to jump down at the boundary. Nevertheless, we show that the presence of arbitrarily small space-time white noise due to fluctuations in the incoming particles surprisingly eliminates all nonlinear interactions in the model and thus has the potential to stabilize the dynamics and suppress the growth of hills in these models.