Ten Lectures on Random Media: 32 (Oberwolfach Seminars, 32) - Softcover

Bolthausen, Erwin; Sznitman, Alain-Sol

Softcover

ISBN 10: 3764367032 ISBN 13: 9783764367039

Publisher: Birkhäuser, 2002

Synopsis

The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolfach, and in February-March 2000 at the Ecole Normale Superieure in Paris. In both places the atmosphere was very friendly and stimulating. The positive response of the audience was encouragement enough to write up these notes. I hope they will carryover the enjoyment of the live lectures. I whole heartedly wish to thank Profs. Matthias Kreck and Jean-Franc;ois Le Gall who were respon­ sible for these two very enjoyable visits, Laurent Miclo for his comments on an earlier version of these notes, and last but not least Erwin Bolthausen who was my accomplice during the DMV-Seminar. A Brief Introduction The main theme of this series of lectures are "Random motions in random me­ dia". The subject gathers a variety of probabilistic models often originated from physical sciences such as solid state physics, physical chemistry, oceanography, biophysics . . . , in which typically some diffusion mechanism takes place in an inho­ mogeneous medium. Randomness appears at two levels. It comes in the description of the motion of the particle diffusing in the medium, this is a rather traditional point of view for probability theory; but it also comes in the very description of the medium in which the diffusion takes place.

About this title

Synopsis

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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2002
• Language: English
• ISBN 10: 3764367032
• ISBN 13: 9783764367039
• Binding: Paperback
• Number of pages: 122