  We study the effect of the non-Gaussianity induced by gravitational evolution
upon the statistical properties of absorption in quasar (QSO) spectra. Using
the generic hierarchical ansatz and the lognormal approximation we derive the
analytical expressions for the one-point PDF as well as for the joint two-point
probability distribution (2PDF) of transmitted fluxes in two neighbouring QSOs.
These flux PDFs are constructed in 3D as well as in projection (i.e. in 2D).
The PDFs are constructed by relating the lower-order moments, i.e. cumulants
and cumulant correlators, of the fluxes to the 3D neutral hydrogen distribution
which is, in turn, expressed as a function of the underlying dark matter
distribution. The lower-order moments are next modelled using a generating
function formalism in the context of a {\em minimal tree-model} for the
higher-order correlation hierarchy. These different approximations give nearly
identical results for the range of redshifts probed, and we also find a very
good agreement between our predictions and outputs of hydrodynamical
simulations. The formalism developed here for the joint statistics of
flux-decrements concerning two lines of sight can be extended to multiple lines
of sight, which could be particularly important for the 3D reconstruction of
the cosmic web from QSO spectra (e.g. in the BOSS survey). These statistics
probe the underlying projected neutral hydrogen field and are thus linked to
"hot-spots" of absorption. The results for the PDF and the bias presented here
use the same functional forms of scaling functions that have previously been
employed for the modelling of other cosmological observation such as the
Sunyaev-Zel'dovich effect.
