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The field of random media has been the object of intensive mathematical research over the last thirty years. It covers a variety of models, mainly from condensed matter physics, physical chemistry, and geology, where one is interested in materials which have defects or inhomogeneities. These features are taken into account by letting the medium be random.

It has been found that this randomness can cause very unexpected effects in the large scale behavior of these models; on occasion these run contrary to the prevailing intuition.  A feature of this area, which it has in common with other areas of statistical physics, is that what was initially thought to be just a simple toy model has turned out to be a major mathematical challenge.