in the position of the front between different events. It reads [@BDMM] $$\langle {\cal I}_y^2\rangle -\langle {\cal I}_y\rangle^2=
\frac{\pi^4\chi^{\prime\prime}(\gamma_0)}{3\ln^3(1/\alpha^2)}
y+\cdots
\label{variance}$$ While again the exact value will not be probed for it is too much asymptotic, the characteristic feature of the variance of the position of the front is that it scales linearly with $y$. We recall that this linearly growing variance is at the origin of the phenomenon of “diffusive scaling” in the observable amplitude, which breaks geometric scaling predicted that comes out of the solution to the BK equation.

As for the case when evolution does not include a saturation mechanism in the Fock states, it is difficult to figure out a priori what is going to happen. We will find out in the next section by performing numerical simulations of the different variants of the model.

\[sec4\]Numerical study of the toy model
========================================

We have implemented the model defined in Secs. \[sec2\] and \[sec3\] in the form of a Monte-Carlo event generator. There was no major difficulty to be overcome: The techniques that we have used are standard and the code can easily be reproduced by the reader.

The evolution starts with one particle on a given 