  We study the distribution of interfacial separations P(u) at the contact
region between two elastic solids with randomly rough surfaces. An analytical
expression is derived for P(u) using Persson's theory of contact mechanics, and
is compared to numerical solutions obtained using (a) a half-space method based
on the Boussinesq equation, (b) a Green's function molecular dynamics technique
and (c) smart-block classical molecular dynamics. Overall, we find good
agreement between all the different approaches.
