  Within the framework of a (1+1)-dimensional model which mimics evolution and
scattering in QCD at high energy, we study the influence of the running of the
coupling on the high-energy dynamics with Pomeron loops. We find that the
particle number fluctuations are strongly suppressed by the running of the
coupling, by at least one order of magnitude as compared to the case of a fixed
coupling, for all the rapidities that we have investigated, up to Y=200. This
reflects the slowing down of the evolution by running coupling effects, in
particular, the large rapidity evolution which is required for the formation of
the saturation front via diffusion. We conclude that, for all energies of
interest, processes like deep inelastic scattering or forward particle
production can be reliably studied within the framework of a mean-field
approximation (like the Balitsky-Kovchegov equation) which includes running
coupling effects.
