  The diffusion and coalescence of individual atoms on a nanostructured surface
are treated in a purely statistical way. From this, analytical formulas are
derived which, from a known initial state, give the final cluster size
distribution on a surface after the diffusion of all the individual atoms.
Unexpectedly, it turns out that these formulas allow obtaining a statistical
law giving the size histogram of the clusters when only homogeneous nucleation
occurs with a critical germ equal to 2, and in the situation where nucleation
starts once the deposition of the atoms is completed.
