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Brownian Motion, Obstacles and Random Media

  • Book
  • © 1998
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Overview

Authors:
  1. Alain-Sol Sznitman

    1. FIM, ETH Zurich, Zurich, Switzerland

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  • This book presents a very attractive and active field of research.
  • The approach taken is highly original and personal.
  • It is aimed both at graduate students and researchers.

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Some Tools

    1. Front Matter

      Pages 1-1
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    2. The Feynman-Kac Formula and Semigroups

      • Alain-Sol Sznitman
      Pages 3-37
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    3. Some Potential Theory

      • Alain-Sol Sznitman
      Pages 39-89
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    4. Some Principal Eigenvalue Estimates

      • Alain-Sol Sznitman
      Pages 91-136
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  3. Brownian Motion and Random Obstacles

    1. Front Matter

      Pages 141-141
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    2. The Method of Enlargement of Obstacles

      • Alain-Sol Sznitman
      Pages 143-215
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    3. Lyapunov Exponents

      • Alain-Sol Sznitman
      Pages 217-263
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    4. Quenched Path Measure and Pinning Effect

      • Alain-Sol Sznitman
      Pages 265-312
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    5. Overview, further Results and Problems

      • Alain-Sol Sznitman
      Pages 313-342
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  4. Back Matter

    Pages 343-357
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Keywords

About this book

The principal purpose of this book is to provide an account of the circle of ideas, results and techniques, which emerged roughly over the last ten years in the study of Brownian motion and random obstacles. The accumulation of results in many separate sources eventually made it impractical, if not impossible, for the nonspecialist to gain access to the developments of the subject. This book is an attempt to remedy this situation. Part of the thrill of the investigation of Brownian motion and random obsta­ cles certainly stems from its many connections with various areas of math­ ematics, but also from the formal and mysterious physical heuristics which relate to it. In particular the loose concept of pockets of low local eigenval­ ues plays an important role in the study of Brownian motion and random obstacles, and also represents a paradigm which has natural resonances with several other areas of random media. This last feature has increasingly be­ come clear over the last few years.

Authors and Affiliations

  • FIM, ETH Zurich, Zurich, Switzerland

    Alain-Sol Sznitman

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