  We investigate the error implied by the use of the Zel'dovich approximation
to set up the initial conditions at a finite redshift zi in numerical
simulations. Using a steepest-descent method developed in a previous work we
derive the probability distribution P(delta_R) of the density contrast in the
quasi-linear regime. This also provides its dependence on the redshift zi at
which the simulation is started. Thus, we find that the discrepancy with the
exact pdf (defined by the limit zi->infinity) is negligible after the scale
factor has grown by a factor a/a_i>5, for scales which were initially within
the linear regime with sigma_i>0.1. This shows that the use of the Zel'dovich
approximation to implement the initial conditions is sufficient for practical
purposes since these are not very severe constraints.
