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)= 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.Comment: LaTeX, 4 pages, 3 figure