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Abstract. Random media have material properties with such complicated spatial vari-ations that they can only be described statistically. When looking at waves propagating in these media, we can only expect in general a statistical description of the wave. But sometimes there exists a deterministic result: the wave dynamics only depends on the statistics of the medium, and not on the particular realization of the medium. Such a phe-nomenon arises when the different scales present in the problem (wavelength, correlation length, and propagation distance) can be separated. In this lecture we restrict ourselves to one-dimensional wave problems that arise naturally in acoustics and geophysics