We present results of a numerical renormalization approximation to the self-similar growth of clustering of a collisionless pressureless fluid out of a power-law spectrum of primeval Gaussian mass density fluctuations , P ( k ) \propto k ^ { n } , in an Einstein-de Sitter cosmological model .
The self-similar position two-point correlation function , \xi ( r ) , seems to be well established .
The renormalization solutions for \xi ( r ) show a satisfying insensitivity to the parameters in the method , and at n = -1 and n = 0 are quite close to the Hamilton et al . formula for interpolation between the large-scale perturbative limit and stable small-scale clustering .
The solutions are tested by the comparison of the mean relative peculiar velocity \langle v _ { ij } \rangle of particle pairs ( ij ) and the velocity derived from \xi ( r ) under the assumption of self-similar evolution .
Both the renormalization and a comparison conventional N-body solution are in reasonable agreement with the test , although the conventional approach does slightly better at large separations and the renormalization approach slightly better at small separations .
Other comparisons of renormalization and conventional solutions are more demanding and the results much less satisfactory .
Maps of the particle positions in redshift space in the renormalization solutions show more nearly empty voids and less prominent walls than do comparison conventional N-body solutions .
The rms relative velocity dispersion is systematically smaller in the renormalization solution ; the difference approaches a factor of two on small scales .
There also are substantial differences in the frequency distributions of clump masses in renormalization and conventional solutions .
The third moment S _ { 3 } from the distribution of mass within cells is in reasonable agreement with second-order perturbation theory on large scales , while on scales less than the clustering length S _ { 3 } is roughly consistent with hierarchical clustering but is heavily affected by shot noise .