Ten Lectures on Random Media

1. Front Matter

   Pages i-vii

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2. Lectures on Random Motions in Random Media

   1. Front Matter

      Pages 1-3

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   2. A Brief Introduction

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 5-7

   3. The Environment Viewed from the Particle

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 9-15

   4. Central Limit Theorem for Random Walks in Random Environment with Null Drift

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 16-22

   5. Long Time Survival among Random Traps

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 23-31

   6. Multi-Dimensional Random Walks in Random Environment

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 32-39

   7. More on Random Walks in Random Environment

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 40-51

3. Lectures on Spin Glasses

   1. Front Matter

      Pages 53-53

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   2. On the Sherrington-Kirkpatrick Model of Spin Glasses

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 55-63

   3. The Sherrington-Kirkpatrick Model: High Temperature and Nonzero Magnetic Field

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 64-73

   4. The Random Energy Model

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 74-82

   5. The Generalized Random Energy Model and Induced Clusterings

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 83-95

   6. Markovian Clustering, Reshuffling, and a Self-Consistency Equation

      • Erwin Bolthausen, Alain-Sol Sznitman

      Pages 96-109

4. Back Matter

   Pages 111-119

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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.

• Mathematica
• disordered systems
• probability
• probability theory
• random walk
• statistical physics

• Institute for Applied Mathematics, University of Zurich, Zürich, Switzerland

  Erwin Bolthausen

• Department of Mathematics, ETH Zentrum, Zürich, Switzerland

  Alain-Sol Sznitman

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