Fluctuating pulled fronts and Pomerons

I present a pedagogical 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 explain 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. I also discuss the diagrammatic interpretation of the particle number fluctuations in terms of Pomeron loops