Edwards-Wilkinson equation from lattice transition rules.

Continuum equations of motion for the height fluctuations of lattice growth models are derived from their transition rules by regularizing and coarse-graining the associated discrete Langevin equations. For models with random deposition followed by instantaneous relaxation to a neighboring site based on identifying the local height minimum, our methodology yields the Edwards-Wilkinson equation. The application of this procedure to other growth models is discussed.