  In this article we reconsider the problem of the propagation of waves in a
random medium in a kinetic regime. The final aim of this program would be the
understanding of the conditions which allow to derive a kinetic or radiative
transfer equation. Although it is not reached for the moment, accurate and
somehow surprising number estimates in the Fock space setting, which happen to
be propagated by the dynamics on macroscopic time scales, are obtained. Keel
and Tao endpoint Strichartz estimates play a crucial role after being combined
with a Cauchy-Kowalevski type argument. Although the whole article is focussed
on the simplest case of Schr{\"o}dinger waves in a gaussian random potential of
which the translation into a QFT problem is straightforward, several
intermediate results are written in a general setting in order to be applied to
other similar problems.
