individual scatterings, and that each of them occurs with probability $\alpha^2$ if the objects in presence have the same position on the lattice, and with probability 0 if this is not the case. Note that there is here a difference with the QCD dipole model since there, the interaction consists in at most one gluon exchange between each pair of dipoles, whereas with our choice any number of exchanges may occur.

Let us consider two particles, initially at respective sites $0$ and $i$, which evolve into systems of $n_j(y)$ and $m_{j}(y)$ particles respectively on site $j$ after a boost at rapidity $y$. In the Mueller approach [@M2; @M3], the $S$-matrix for the scattering of these objects is defined, for low rapidities, as $$S(y,i)=\left\langle\prod_j e^{-\alpha^2 n_j(\sigma y) m_{j}
((1-\sigma)y)}
\right\rangle
\label{mueller}$$ where the average is taken over the realizations of the two systems. The $i$ index is implicit in the r.h.s.: It is related to the initial condition that leads, after evolution, to the system $\{m_j\}$. $\sigma$ ranges between 0 and 1 and defines the share of the rapidity between the two systems. When $\sigma=0$ (or 1: the target and the projectile may be exchanged, hence there is a symmetry $\sigma\rightarrow 