  Within the framework of a (1+1)--dimensional model which mimics high energy
QCD, we study the behavior of the cross sections for inclusive and diffractive
deep inelastic $\gamma^*h$ scattering cross sections. We analyze the cases of
both fixed and running coupling within the mean field approximation, in which
the evolution of the scattering amplitude is described by the
Balitsky-Kovchegov equation, and also through the pomeron loop equations, which
include in the evolution the gluon number fluctuations. In the diffractive
case, similarly to the inclusive one, the suppression of the diffusive scaling,
as a consequence of the inclusion of the running of the coupling, is observed.

High Energy Physics - Phenomenology