Random growth of interfaces as a subordinated process

We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y (t) identical with h (t)- , which is depicted as being subordinated to a standard fluctuation-dissipation process with friction gamma. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y (0) =0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the (1+1) -dimensional model of ballistic deposition is remarkably good, in spite of the finite-size effects affecting this model.