  We propose a stochastic particle model in (1+1)-dimensions, with one
dimension corresponding to rapidity and the other one to the transverse size of
a dipole in QCD, which mimics high-energy evolution and scattering in QCD in
the presence of both saturation and particle-number fluctuations, and hence of
Pomeron loops. The model evolves via non-linear particle splitting, with a
non-local splitting rate which is constrained by boost-invariance and multiple
scattering. The splitting rate saturates at high density, so like the gluon
emission rate in the JIMWLK evolution. In the mean field approximation obtained
by ignoring fluctuations, the model exhibits the hallmarks of the BK equation,
namely a BFKL-like evolution at low density, the formation of a traveling wave,
and geometric scaling. In the full evolution including fluctuations, the
geometric scaling is washed out at high energy and replaced by diffusive
scaling. It is likely that the model belongs to the universality class of the
reaction-diffusion process. The analysis of the model sheds new light on the
Pomeron loops equations in QCD and their possible improvements.
