Dense-dilute factorization for a class of stochastic processes and for high energy QCD

Stochastic processes described by evolution equations in the universality class of the Fisher-Kolmogorov-Petrovsky-Piscounov equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model with no spatial dimensions and we illustrate it numerically on a one-dimensional toy model that possesses some of the main features of high energy QCD evolution. We explain how this procedure may be applied to QCD amplitudes, by combining Salam's Monte Carlo implementation of the dipole model and a numerical solution of the Balitsky-Kovchegov equation.