our comments will always refer to the traveling wave that propagates along the positive $i$ axis.

We see that the fastest wave is observed in the BK model, while the saturation model gives rise to the slowest one. We also observe that all waves get slanted during their propagation, except in the BK model. This is “diffusive scaling”, while the BK solutions exhibit geometric scaling.

In the next paragraphs, we go deeper into the analysis of this calculation by focussing on the statistics of the position of the front: Its mean velocity and its variance, for the different variants of the model.

BK equation
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We go to the lab frame, that is, we put all the rapidity evolution in one of the objects, while the other one is at rest. Multiple scatterings off a system that does not saturate gives a $S$-matrix that solves the BK equation,[^4] and hence that has the form of a traveling wave whose characteristics are given in Sec. \[sec2B\]. The velocity of the front is presented in Fig. \[fig:bk\] for $1/\alpha^2=20$. In order to interpret the results, it is useful to compute the numerical values of $y_F$ and $y_R$ in Eq. (\[yF\]) and (\[yR\]): 