  The conventional and linearly polarized Weizs\"acker-Williams gluon
distributions at small x are defined from the two-point function of the gluon
field in light-cone gauge. They appear in the cross section for dijet
production in deep inelastic scattering at high energy. We determine these
functions in the small-x limit from solutions of the JIMWLK evolution equations
and show that they exhibit approximate geometric scaling. Also, we discuss the
functional distributions of these WW gluon distributions over the JIMWLK
ensemble at rapidity $Y\sim 1/\alpha_s$. These are determined by a 2d Liouville
action for the logarithm of the covariant gauge function $g^2
\mathrm{tr}\,A^+(q)A^+(-q)$. For transverse momenta on the order of the
saturation scale we observe large variations across configurations (evolution
trajectories) of the linearly polarized distribution up to several times its
average, and even to negative values.
