ZELDOVICH APPROXIMATION AND THE PROBABILITY-DISTRIBUTION FOR THE SMOOTHED DENSITY FIELD IN THE NONLINEAR REGIME

The study of large-scale structures in the universe is often based on the observed density distribution of matter smoothed by a suitable fil ter function. The probability distribution for this smoothed density f ield in the nonlinear regime is studied using the Zel'dovich approxima tion. When the shear term of the velocity field is not too large, one can obtain a reasonably good analytic approximation to this probabilit y distribution. The properties of this distribution are discussed and compared with other attempts along similar lines.