  A set of scaling laws, based on the stochastic motions of the granular
components of astronomical systems, is applied to a cosmological model with a
positive cosmological constant. It follows that the mass of the dominant
particle in the observable universe must be proportional to the sixth root of
the cosmological constant and of the order of the nucleon mass, which is
consistent with the Zeldovich scaling law. The approach is a natural way to
solve the cosmic coincidence problem. On the other hand, the observed value of
the cosmological constant emerges as the result of a scaling law induced by the
stochastic mechanism which gives rise to the gravitationally bound systems.
