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It is known that a nonabsorbing one-dimensional semi-infinite random medium is totally reflecting. In connection with this, when the medium is subject to monochromatic excitation with an arbitrary frequency, well-localized "stochastic resonances" may appear, at which the wave amplitude can exceed any given value, with nonzero probability in such a way as to make the mean energy density inside the medium infinite. The problem is considered both for continuous media (e.g., a random elastic bar) and discrete media (e.g., disordered linear atomic chains).
Frisch et al. (Sat,) studied this question.