Langevin approach to interface statistics and diffusion-limited reactions

In this paper we study the linear Langevin equation related to interface-growth phenomena and to diffusion-limited reactions. Using a discretized scheme and the Chapman-Kolmogorov relation, we derive an expression for the time evolution of the mean-squared fluctuations, an expression valid both for Euclidean and fractal lattices. The theoretical analysis is corroborated by numerical investigations carried out for Euclidean lattices and fractals.