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We examine numerically different zero-dimensional reaction-diffusionprocesses as candidate toy models for high-energy QCD evolution. Of the modelsexamined -- Reggeon Field Theory, Directed Percolation and Reversible Processes-- only the latter shows the behaviour commonly expected, namely an increase ofthe scattering amplitude with increasing rapidity. Further, we find thatincreasing recombination terms, quantum loops and the heuristic inclusion of arunning of the couplings, generically slow down the evolution.

Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD