difference between saturation and bare multiple scatterings. The saturation scheme leads to linearly increasing fluctuations as soon as the front is formed, in qualitative agreement with Eq. (\[variance\]). By contrast, the bare multiple-scattering schemes lead to fluctuations that slow down with $y$. However, there is a range in rapidity in which the variances agree in the different models and in all frames, except for the lab frame which has systematically less fluctuations. The agreement is particularly striking at large $1/\alpha^2$. The range in which the models match can be estimated as $y<2 y_F$ for the center-of-mass frame, if $y_F$ is taken to the rapidity at which the front is effectively formed (around the local maximum in the variance) rather than the numerical estimate done before.

The fact that the calculations in the lab frame lead to different front velocities and quite different fluctuations should maybe not come as a surprise, since the way in which we treat this frame is very special: Indeed, we do not allow at all fluctuations in one of the incoming objects, which is quite unphysical (quantum objects should be allowed to fluctuate even if they have a vanishing rapidity), and which is likely to reduce 