Weakly random media affect propagation of waves and particles over long distances in a non-trivial way. When medium correlations decay rapidly the long time behavior is reasonably well understood: both waves and particles behave, loosely speaking, diffusively, and most non-trivial phenomena happen on the same time scale. I plan to describe interesting new effects in these problems arising from the slow decay of media correlations. This is a joint work with T. Komorowski.
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