  We consider a strictly convex billiard table with $C^2$ boundary, with the
dynamics subjected to random perturbations. Each time the billiard ball hits
the boundary its reflection angle has a random perturbation. The perturbation
distribution corresponds to the physical situation where either the scale of
the surface irregularities is smaller than but comparable to the diameter of
the reflected object, or the billiard ball is not perfectly rigid. We prove
that for a large class of such perturbations the resulting Markov chain is
uniformly ergodic, although this is not true in general.

Dynamical Systems;Probability