A new method to study stochastic growth equations: application to the Edwards-Wilkinson equation

In this work we introduce a method to study stochastic growth equations, which follows a dynamics based on cellular automata modeling. The method defines an interface growth process that depends on height differences between neighbors. The growth rules assign a probability p i(t) for site i to receive a particle at time t, where p i(t) = rho exp[kGi(t)]. Here r and k are two parameters and gammai(t) is a kernel that depends on height h i(t) of site i and on heights of its neighbors, at time t. We specify the functional form of this kernel by the discretization of the d...