Ten lectures on random media. (English) Zbl 1075.60128

Bolthausen, Erwin; Sznitman, Alain-Sol

DMV Seminar 32. Basel: Birkhäuser (ISBN 3-7643-6703-2/pbk). 116 p. (2002).

From the text: The field of random media has been the object of intensive activity over the last twenty-five years. It 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 behavior 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 twenty years of intensive research in this field, certain new paradigms and some general methods have emerged, and the surprising results on the asymptotic behavior 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 tries to give 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. It will be a valuable resource for postgraduates and researchers in probability theory and mathematical physics.

MSC:

60K37	Processes in random environments
60-02	Research exposition (monographs, survey articles) pertaining to probability theory
60K35	Interacting random processes; statistical mechanics type models; percolation theory
82-02	Research exposition (monographs, survey articles) pertaining to statistical mechanics
82B41	Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82B44	Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics