Analysis of Cosmological Generalized Reduced Void Probability Functions
  Constrained by Observations and Numerical Simulations
  Using survey data and numerical LCDM modeling we establish an optimized fit
to the generalized Reduced Void Probability Function, RVPF, of Mikjian used to
establish a statistical foundation to any physical process associated with
hierarchical clustering. We use a numerical N-body cosmological simulation
code, GADGET-2, to investigate the sensitivity of the distribution of voids
characterized by the RVPF to a general hierarchical reduced void parameter, a.
The void parameter is related to the Levy stability index of the distribution
and Fischer critical exponent used in clustering models. We numerically
simulate the evolution of the universe from a redshift of z=50 to the current
epoch at z=0 in order to generate RVPFs. GADGET-2 is an N-body/smoothed
particle hydrodynamics, SPH, code that we ran in MPI parallelizable mode on an
HPC Beowulf cluster. The numerical data sets are compared to observational data
from the Sloan digital sky Survey, SDSS, CfA, the Deep2 Galaxy Redshift Survey,
and the 2dF Survey. We find the best value of the parameter a occurs near the
Negative Binomial reduced void probability function but exhibits a departure
from perfect scaling over the z values studied.
