  We argue that large fluctuations in the saturation momentum are necessary to
explain the ATLAS and ALICE data on pA collisions measured at the LHC. Using a
form for the distribution of fluctuations motivated by theoretical studies of
the non-linear evolution equations for the Color Glass Condensate, we find a
remarkably good agreement between theory and the measured distributions. If the
saturation momentum fluctuates, we argue that the cross section for a proton
probe should also fluctuate, consistent with previous observations. Finally we
discuss these results and their possible consistency with what is known about
multiplicity fluctuations in such collisions, and attempts to describe the
ridge effect from properties of the initial state.
