Probability distribution of density fluctuations in the non-linear regime
We present a general procedure for obtaining the present density fluctuation probability distribution given the statistics of the initial conditions. The main difficulties faced with regard to this problem are those related to the non-linear evolution of the density fluctuations and those posed by the fact that the fields we are interested in are the result of filtering an underlying field with structure down to scales much smaller than that of filtering. The solution to the latter problem is discussed here in detail and the solution to the former is taken from a previous work. We have checked the procedure for values of the rms density fluctuation as large as 3/2 and several power spectra and found that it leads to results in excellent agreement with those obtained in numerical simulations. We also recover all available exact results from perturbation theory.