The cloud-in-cloud problem for non-Gaussian density fields

The cloud-in-cloud problem is studied in the context of the extension to non-Gaussian density fields of the PS approach for the calculation of the mass function. As an example of a non-Gaussian probability distribution function (PDF), we consider the chi-square distribution with various degrees of freedom. We generate density fields in cubic boxes with periodic boundary conditions, and then determine the number of points considered collapsed at each scale through a hierarchy of smoothing windows. We find that the mass function we obtain differs from that predicted using the extended PS formalism, particularly for low values of σ and for those PDFs that differ most from a Gaussian.