  Based on the fundamental interplay between spatial wavefronts and
polarization degrees of freedom, spin-orbit interactions (SOI) of light
constitute a novel tool for optical control at the nanoscale. While well
described in simple geometries, SOI of light in disordered environments, where
only a partial knowledge of the material's microscopy is available, remain
largely unexplored. Here, we show that in transversally random media, the
disorder correlation can be exploited to tailor a variety of trajectories for
ballistic beams via SOI. In particular, we unveil the existence of an
oscillating spin Hall effect, stemming from the deformation of the phase of the
wavefront due to SOI. In combination with a weak measurement, this phenomenon
can also be maximized by an optimal choice of the disorder correlation.
