Fractal large-scale structure from a stochastic scaling law model
  A stochastic model relating the parameters of astrophysical structures to the
parameters of their granular components is applied to the formation of
hierarchical, large-scale structures from galaxies assumed as point-like
objects. If the density profile of galaxies on a given scale is described by a
power law then the stochastic model leads naturally to a mass function that is
proportional to the square of the distance from an occupied point, which
corresponds to a two-point correlation function that is inversely proportional
to the distance. This result is consistent with observations indicating that
galaxies are, on the largest scales, characterized by a fractal distribution
with a dimension of order 2 and well-fit with transition to homogeneity at
cosmological scales.
