Ten Lectures on Random Media

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The field of random media gathers a variety of models generally originating from physical sciences, where certain materials or substances have defects or inhomogeneities. This feature can be taken into account by letting the medium be random. Randomness in the medium turns out to cause very unexpected effects, especially in the large-scale behaviour of some of these models. What in the beginning was often deemed to be a simple toy-model ended up as a major mathematical challenge. After more than 25 years of intensive research in this field, certain new paradigms and some general methods have emerged, and the surprising results on the asymptotic behaviour of individual models are now better understood in more general frameworks. This monograph grew out of the DMV lectures on random media held by the authors at the Mathematical Research Institute in Oberwolfach in November 1999 and gives an account of some of the developments in the field, especially in the area of random motions in random media and of mean-field spin glasses. Postgraduates and researchers in probability theory and mathematical physics should find it a valuable resource.