Pure and applied stochastic analysis and random fields form the subject of this book. The collection of articles on these topics represent the state of the art of the research in the field, with particular attention being devoted to stochastic models in finance. Some are review articles, others are original papers; taken together, they will apprise the reader of much of the current activity in the area.

Pure and applied stochastic analysis and random fields form the subject of this book. The collection of articles on these topics represent the state of the art of the research in the field, with particular attention being devoted to stochastic models in finance. Some are review articles, others are original papers; taken together, they will apprise the reader of much of the current activity in the area.

Spin glass theory is going through a stunning period of progress while finding exciting new applications in areas beyond theoretical physics, in particular in combinatorics and computer science. This collection of state-of-the-art review papers written by leading experts in the field covers the topic from a wide variety of angles. The topics covered are mean field spin glasses, including a pedagogical account of Talagrand's proof of the Parisi solution, short range spin glasses, emphasizing the open problem of the relevance of the mean-field theory for lattice models, and the dynamics of spin glasses, in particular the problem of ageing in mean field models.

The book will serve as a concise introduction to the state of the art of spin glass theory, 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 new volume of the long-established St. Flour Summer School of Probability includes the notes of the three major lecture courses by Erwin Bolthausen on "Large Deviations and Iterating Random Walks", by Edwin Perkins on "Dawson-Watanabe Superprocesses and Measure-Valued Diffusions", and by Aad van der Vaart on "Semiparametric Statistics".

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."