High energy asymptotics of scattering processes in QCD

High energy scattering in the QCD parton model was recently shown to be a reaction-diffusion process and, thus, to lie in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the latter appears naturally in the context of the parton model. We provide a thorough numerical analysis of the mean-field approximation, given in QCD by the Balitsky-Kovchegov equation. In the framework of a simple stochastic toy model that captures the relevant features of QCD, we discuss and illustrate the universal properties of such stochastic models. We investigate, in particular, the validity of the mean-field approximation and how it is broken by fluctuations. We find that the mean-field approximation is a good approximation in the initial stages of the evolution in rapidity.