This book serves as a concise introduction to the state-of-the-art of spin glass theory. The collection of review papers are written by leading experts in the field and cover the topic from a wide variety of angles. The book will be useful to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.
This volume features lectures from the Saint-Flour Summer School of Probability Theory held from July 8 to 24, 1999. The authors are acknowledged for their significant contributions, and their lectures serve as a valuable reference in the field. The event attracted 85 participants, with 31 presenting their research. A list of participants and their papers is included at the end of the volume. Additionally, to aid in research related to previous schools, we provide the volume numbers of the "Lecture Notes" where they can be found: Lecture Notes in Mathematics spans various years from 1971 to 1998, with specific volume numbers listed for each year. The content includes significant topics such as large deviations and interacting random walks, featuring works by Erwin Bolthausen on subjects like the construction of three-dimensional polymer measures, self-attracting random walks, and one-dimensional pinning-depinning transitions. Each section is accompanied by references for further exploration.
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.