  We develop a non-perturbative method to derive the probability distribution
$P(\delta_R)$ of the density contrast within spherical cells in the
quasi-linear regime. Indeed, since this corresponds to a rare-event limit a
steepest-descent approximation can yield asymptotically exact results. We check
that this is the case for Gaussian initial density fluctuations, where we
recover most of the results obtained by perturbative methods from a
hydrodynamical description. Moreover, we correct an error which was introduced
in previous works for the high-density tail of the pdf. This feature, which
appears for power-spectra with a slope $n<0$, points out the limitations of
perturbative approaches which cannot describe the pdf $P(\delta_R)$ for
$\delta_R \ga 3$ even in the limit $\sigma \to 0$. This break-up does not
involve shell-crossing and it is naturally explained within our framework.
Thus, our approach provides a rigorous treatment of the quasi-linear regime,
which does not rely on the hydrodynamical approximation for the equations of
motion. Besides, it is actually simpler and more intuitive than previous
methods. Our approach can also be applied to non-Gaussian initial conditions.
