Nonlinear clustering in the CfA redshift survey

The probability of finding a hole in a randomly placed sphere of volume V has been considered in the Cfa survey by numerous authors. The main emphasis of these studies has been on a scaling law derived from the assumption of hierarchical clustering. Here, the counts in cell statistics P(N) in the CfA redshift survey are analyzed. The results show that the general behavior of the P(N) can be predicted on the sole assumption of the hierarchical hypothesis. Scaling forms can then be predicted which appear to be verified to a fairly good extent in the Cfa redshift survey. This implies that the hypothesis of scale-invariant many-body correlations function provides for a satisfactory description of the count-in-cell statistics. 23 refs