Dense-dilute factorization for a class of stochastic processes and for high energy QCD
Abstract
Description
Stochastic processes described by evolution equations in the universality class of the FKPP 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.
9 pages. v2: Eq.(4) corrected, numerics improved, various clarifying comments added. Conclusions unchanged. v3: comments and references added, many misprints fixed
9 pages. v2: Eq.(4) corrected, numerics improved, various clarifying comments added. Conclusions unchanged. v3: comments and references added, many misprints fixed