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Brownian Motion, Obstacles and Random Media

  • Alain-Sol Sznitman

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

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Some Tools

    1. Front Matter
      Pages 1-1
    2. Alain-Sol Sznitman
      Pages 3-37
    3. Alain-Sol Sznitman
      Pages 39-89
    4. Alain-Sol Sznitman
      Pages 91-136
  3. Brownian Motion and Random Obstacles

    1. Front Matter
      Pages 141-141
    2. Alain-Sol Sznitman
      Pages 143-215
    3. Alain-Sol Sznitman
      Pages 217-263
    4. Alain-Sol Sznitman
      Pages 265-312
    5. Alain-Sol Sznitman
      Pages 313-342
  4. Back Matter
    Pages 343-357

About this book

Introduction

This book is aimed at graduate students and researchers. It provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. This subject has a rich phenomenology which exhibits certain paradigms, emblematic of the theory of random media. It also brings into play diverse mathematical techniques such as stochastic processes, functional analysis, potential theory, first passage percolation. In a first part, the book presents, in a concrete manner, background material related to the Feynman-Kac formula, potential theory, and eigenvalue estimates. In a second part, it discusses recent developments including the method of enlargement of obstacles, Lyapunov coefficients, and the pinning effect. The book also includes an overview of known results and connections with other areas of random media.

Keywords

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

Authors and affiliations

  • Alain-Sol Sznitman
    • 1
  1. 1.FIMETH ZurichZurichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-11281-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08420-1
  • Online ISBN 978-3-662-11281-6
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site