not tuned to data, and are in addition limited to gluons, the model is naturally less accurate than  the [P]{}and models. Our aim has instead been focused on understanding the dynamics of small-$x$ evolution and saturation, including correlations and fluctuations,  in connection with multiple parton interactions [@Flensburg:2011kj] and diffraction [@Flensburg:2010kq; @Flensburg:2012zy]. The formulation in transverse coordinate space makes the model particularly suited for studies of string interference and rope formation. Although it has also been applied to collisions with nuclei (see  refs. [@Flensburg:2011wx; @Flensburg:2012zz]), we will in this paper limit our study to proton–proton collisions.

We will here assume that colour ropes can form by coherent interaction between a group of strings confined within a limited transverse size. As in ref. [@Biro:1984] we assume random colour charges for the individual strings, leading to a random walk in colour space. We also assume that the rope breaks by successive production of new $q\bar{q}$ pairs. The nature of the tunneling process implies here that an “effective string tension” is determined by the *reduction* in rope tension in each individual breakup. As mentioned in ref. [@Biro:1984], and discussed in detail below, the result of the rope formation is then a smaller number of 