  The main observed properties of Ly-$\alpha$ absorbers are investigated on the
basis of theoretical model of formation and evolution of DM structure elements.
This model is generally consistent with simulations of absorbers formation and
with statistical description of structure evolution based on the Zel'dovich
theory. The analysis of redshift variations of comoving linear number density
of absorbers was performed in our previous paper.
  We show that the observed characteristics of Doppler parameter can be related
to the size of DM structure elements what allows us to explain the observed
distribution of Doppler parameter. This distribution is found to be consistent
with the Gaussian initial perturbations. The observed characteristics of
entropy and column density, $N_{HI}$, confirm that merging of pancakes is the
main evolutionary process at redshifts $z\geq 2$. The observed sample of
absorbers characterizes mainly the matter distribution within large low density
regions and therefore it is difficult to reconstruct the density field from the
distribution of absorbers.
