  We determine the rate of escape from a potential well, and the diffusion
coefficient in a periodic potential, of a random walker that moves under the
influence of the potential in between successive collisions with the heat bath.
In the overdamped limit, both the escape rate and the diffusion coefficient
coincide with those of a Langevin particle. Conversely, in the underdamped
limit the two dynamics have a different temperature dependence. In particular,
at low temperature the random walk has a smaller escape rate, but a larger
diffusion coefficient.
