  Generalized statistical models of voids and hierarchical structure in
cosmology are developed. The often quoted negative binomial model and
frequently used thermodynamic model are shown to be special cases of a more
general distribution which contains a parameter "a". The parameter is related
to the Levy index alpha and the Fisher critical exponent tau, the latter
describing the power law fall off of clumps of matter around a phase
transition. The parameter"a", exponent tau, or index alpha can be obtained from
properties of a void scaling function. A stochastic probability variable "p" is
introduced into a statistical model which represent the adhesive growth of
galaxy structure. For p<1/2, the galaxy count distribution decays exponential
fast with size. For p>1/2, an adhesive growth can go on indefinitely thereby
forming an infinite supercluster. At p=1/2 a scale free power law distribution
for the galaxy count distribution is present. The stochastic description also
leads to consequences that have some parallels with cosmic string results,
percolation theory and phase transitions.

Astrophysics;Nuclear Theory