  Consider the map $(x, y) \mapsto (x + \epsilon^{-\alpha} \sin (2\pi x) +
\epsilon^{-1-\alpha}z, z + \epsilon \sin(2\pi x))$, which is conjugate to the
Chirikov standard map with a large parameter. The parameter value $\alpha = 1$
is related to "scattering by resonance" phenomena. For suitable $\alpha$, we
obtain a central limit theorem for the slow variable $z$ for a (Lebesgue)
random initial condition. The result is proved by conjugating to the Chirikov
standard map and utilizing the formalism of standard pairs. Our techniques also
yield for the Chirikov standard map a related limit theorem and a "finite-time"
decay of correlations result.
