  This work is devoted to radiative transfer equations with long-range
interactions. Such equations arise in the modeling of high frequency wave
propagation in random media with long-range dependence. In the regime we
consider, the singular collision operator modeling the interaction between the
wave and the medium is conservative, and as a consequence wavenumbers take
values on the unit sphere. Our goals are to investigate the regularizing
effects of grazing collisions, the diffusion limit, and the peaked forward
limit. As in the case where wavenumbers take values in R^{d+1}, we show that
the transport operator is hypoelliptic, so that the solutions are infinitely
differerentiable in all variables. Using probabilistic techniques, we show as
well that the diffusion limit can be carried on as in the case of a regular
collision operator, and as a consequence that the diffusion coefficient is
non-zero and finite. We finally consider the regime where grazing collisions
are dominant.
