Brownian Motion, Obstacles and Random Media

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

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      Pages 3-37

   3. Some Potential Theory

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      Pages 39-89

   4. Some Principal Eigenvalue Estimates

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      Pages 91-136

3. Brownian Motion and Random Obstacles

   1. Front Matter

      Pages 141-141

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   2. The Method of Enlargement of Obstacles

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      Pages 143-215

   3. Lyapunov Exponents

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      Pages 217-263

   4. Quenched Path Measure and Pinning Effect

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      Pages 265-312

   5. Overview, further Results and Problems

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      Pages 313-342

4. Back Matter

   Pages 343-357

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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.

• Brownian bridge
• Brownian motion
• Feynman-Kac formula
• Partial differential equations
• Potential
• Probability
• Random media
• Stochastic processes
• partial differential equation
• quenching
• stochastic process

• FIM, ETH Zurich, Zurich, Switzerland

  Alain-Sol Sznitman

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