  A rough collision law describes the limiting contact dynamics of a pair of
rough rigid bodies, as the scale of the rough features (asperities) on the
surface of each body goes to zero. The class of rough collision laws is quite
large and includes random elements. Our main results characterize the rough
collision laws for a freely moving rough disk and a fixed rough wall in
dimension 2. Any collision law which (i) is symmetric with respect to a certain
well-known invariant measure from billiards theory, and (ii) conserves the
projection of the phase space velocity onto the "rolling velocity" is a rough
collision law. We also provide a method for explicitly constructing rough
collision laws for a broad range of choices of microstructure on the disk and
wall. In our introduction, we review past work in billiards, including
characterizations of other rough billiard systems, which our results build
upon.
