The distribution of counts in cells in the non-linear regime

The Press-Schechter approach is used to provide an approximate description of the counts in cells distribution in the non-linear regime. Simple, illustrative models for the spatial distribution and internal structure of Press-Schechter clumps are assumed. Then, these distributions of non-linear Press-Schechter clumps are smoothed with a large-scale filter. The resulting evolved, smoothed distributions of counts in (large) cells are compared with the predictions of linear and quasi-linear theory. The agreement between these Press-Schechter models and the quasi-linear analyses increases as the initial power on large scales decreases. These simple models are also used to compute estimates of the skewness in the highly non-linear regime. The non-linear, Press-Schechter values of the skewness and higher order moments are scale-dependent, and are in good agreement with the values measured, in the non-linear regime, in N-body simulations. For initial power spectra of current interest, the quasi-linear value of the skewness is always within a factor of two or three of the non-linear values in these models.