  I give a physical discussion of the influence of particle number fluctuations
on the high energy evolution in QCD. I emphasize the event-by-event description
and the correspondence with the problem of `fluctuating pulled fronts' in
statistical physics. I show that the correlations generated by fluctuations
reduce the phase-space for BFKL evolution up to saturation. Because of that,
the evolution `slows down', and the rate for the energy increase of the
saturation momentum is considerably decreased. Also, the stochastic aspects
inherent in fluctuations lead to the breakdown of geometric scaling and of the
BFKL approximation. Finally, I explain the diagrammatic interpretation of the
particle number fluctuations as initiators of the Pomeron loops.
