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We present results of a numerical renormalization approximation to the self-similar growth of clustering of pressureless dust out of a power-law spectrumof primeval Gaussian mass density fluctuations (index n) in an Einstein-deSitter cosmological model. The self-similar two-point correlation function, xi,seems to be well established. The renormalization solutions for xi show asatisfying insensitivity to the parameters in the method, and at n=-1 and 0 areclose to the Hamilton et al. formula for interpolation between the large-scaleperturbative limit and stable small-scale clustering. The solutions are testedby comparing the mean relative peculiar velocity <v_ij> of particle pairs andthe velocity derived from xi under the assumption of self-similar evolution.Both the renormalization and a comparison conventional N-body solution are inreasonable agreement with the test, although the conventional approach doesslightly better at large separations and the renormalization approach slightlybetter at small separations. Other comparisons of renormalization andconventional solutions are more demanding and the results less satisfactory.Maps of particle positions in redshift space in the renormalization solutionsshow more nearly empty voids and less prominent walls than do the conventionalsolutions. The rms relative velocity dispersion is systematically smaller inthe renormalization solution. There also are sizeable differences in thefrequency distributions of clump masses in the renormalization and conventionalsolutions. The third moment S_3 from the distribution of mass within cells isin reasonable agreement with second-order perturbation theory on large scales,while on scales less than the clustering length S_3 is roughly consistent withhierarchical clustering but is heavily affected by shot noise.Comment: 34 pages including 12 figures. AAS Latex v4.0 macro

A Numerical Renormalization Solution for Self‐similar Cosmic Structure Formation