  The effect of a small amount of noise on the standard mapping is considered.
Whenever the standard mapping possesses accelerator modes (where the action
increases approximately linearly with time), the diffusion coefficient contains
a term proportional to the reciprocal of the variance of the noise term. At
large values of the stochasticity parameter, the accelerator modes exhibit a
universal behavior. As a result the dependence of the diffusion coefficient on
the stochasticity parameter also shows some universal behavior.
