We point out an analogy between diffractive electron-nucleus scattering events and realizations of one-dimensional branching random walks selected according to the height of the genealogical tree of the particles near their boundaries. This correspondence is made transparent in an event-by-event picture of diffraction, emphasizing the statistical properties of gluon evolution, from which new quantitative predictions straightforwardly follow: we are able to determine the distribution of the total invariant mass produced diffractively, which is an interesting observable that can potentially be measured at a future electron-ion collider.
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