This work is concerned with the asymptotic analysis of a time-splitting scheme for theSchrödinger equation with a random potential having weak amplitude, fast oscillations intime and space, and long-range correlations. Such a problem arises for instance in thesimulation of waves propagating in random media in the paraxial approximation. Thehigh-frequency limit of the Schrödinger equation leads to different regimes depending onthe distance of propagation, the oscillation pattern of the initial condition, and thestatistical properties of the random medium. We show that the splitting scheme capturesthese regimes in a statistical sense for a time stepsize independent of the frequency.
