  We study diffusion on a periodic billiard table with infinite horizon in the
limit of narrow corridors. An effective trapping mechanism emerges according to
which the process can be modeled by a L\'evy walk combining
exponentially-distributed trapping times with free propagation along paths
whose precise probabilities we compute. This description yields an
approximation of the mean squared displacement of infinite-horizon billiards in
terms of two transport coefficients which generalizes to this anomalous regime
the Machta-Zwanzig approximation of normal diffusion in finite-horizon
billiards [Phys. Rev. Lett. 50, 1959 (1983)].
