Travelling waves and impact-parameter correlations

It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion processes as if the evolutions at different points in the transverse plane became uncorrelated through rapidity evolution. We check this assumption by numerically comparing a toy model with QCD-like impact-parameter dependence to its exact counterpart with uniform evolution in impact-parameter space. We find quantitative differences, but which seem to amount to a mere rescaling of the strong coupling constant. Since the rescaling factor does not show any strong alpha_s-dependence, we conclude that locality is well verified, up to subleading terms at small alpha_s.