  The Reggeon field theory in zero transverse dimensions is investigated. Two
versions of the theory are considered: one that allows at most triple pomeron
interactions and the other that embodies an additional 2-->2 quartic Reggeon
coupling. The behavior of the scattering amplitude at asymptotic rapidities is
obtained in both cases. In an s-channel picture of the high energy scattering
both models can be viewed as reaction-diffusion processes. We derive known
results in Reggeon field theory rather easily using the reaction-diffusion
formalism. We find that some results which are surprising from the Reggeon
field theory point of view turn out to have a simple interpretation from the
reaction-diffusion point of view.
