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Using survey data and numerical LCDM modeling we establish an optimized fitto the generalized Reduced Void Probability Function, RVPF, of Mikjian used toestablish a statistical foundation to any physical process associated withhierarchical clustering. We use a numerical N-body cosmological simulationcode, GADGET-2, to investigate the sensitivity of the distribution of voidscharacterized by the RVPF to a general hierarchical reduced void parameter, a.The void parameter is related to the Levy stability index of the distributionand Fischer critical exponent used in clustering models. We numericallysimulate the evolution of the universe from a redshift of z=50 to the currentepoch at z=0 in order to generate RVPFs. GADGET-2 is an N-body/smoothedparticle hydrodynamics, SPH, code that we ran in MPI parallelizable mode on anHPC Beowulf cluster. The numerical data sets are compared to observational datafrom 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 theNegative Binomial reduced void probability function but exhibits a departurefrom perfect scaling over the z values studied.

Analysis of Cosmological Generalized Reduced Void Probability Functions Constrained by Observations and Numerical Simulations