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© 1999

Scaling Limits of Interacting Particle Systems

Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 320)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Claude Kipnis, Claudio Landim
    Pages 1-6
  3. Claude Kipnis, Claudio Landim
    Pages 7-20
  4. Claude Kipnis, Claudio Landim
    Pages 21-40
  5. Claude Kipnis, Claudio Landim
    Pages 41-46
  6. Claude Kipnis, Claudio Landim
    Pages 47-66
  7. Claude Kipnis, Claudio Landim
    Pages 115-139
  8. Claude Kipnis, Claudio Landim
    Pages 141-189
  9. Claude Kipnis, Claudio Landim
    Pages 191-229
  10. Claude Kipnis, Claudio Landim
    Pages 231-256
  11. Claude Kipnis, Claudio Landim
    Pages 257-285
  12. Claude Kipnis, Claudio Landim
    Pages 287-310
  13. Back Matter
    Pages 311-445

About this book

Introduction

The idea of writing up a book on the hydrodynamic behavior of interacting particle systems was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the spring of 1988. At this time Claude wrote some notes in French that covered Chapters 1 and 4, parts of Chapters 2, 5 and Appendix 1 of this book. His intention was to prepare a text that was as self-contained as possible. lt would include, for instance, all tools from Markov process theory ( cf. Appendix 1, Chaps. 2 and 4) necessary to enable mathematicians and mathematical physicists with some knowledge of probability, at the Ievel of Chung (1974), to understand the techniques of the theory of hydrodynamic Iimits of interacting particle systems. In the fall of 1991 Claude invited me to complete his notes with him and transform them into a book that would present to a large audience the latest developments of the theory in a simple and accessible form. To concentrate on the main ideas and to avoid unnecessary technical difficulties, we decided to consider systems evolving in finite lattice spaces and for which the equilibrium states are product measures. To illustrate the techniques we chose two well-known particle systems, the generalized exclusion processes and the zero-range processes. We also conceived the book in such a manner that most chapters can be read independently of the others. Here are some comments that might help readers find their way.

Keywords

Dirichlet form Feynman-Kac formula Hydrodynamic Limits Interacting Particle Systems Markov chain Markov process Martingale Maxima Stochastic p interacting particle system mathematical physics random walk reversible dynamics stochastic process

Authors and affiliations

  1. 1.Instituto de Matematica Pura e AplicadaRio de JaneiroBrasil
  2. 2.CNRS UPRES-A 6085Université de RouenMont Saint Aignan CedexFrance

Bibliographic information

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Reviews

"Das Buch ist nach Meinung des Rezensenten eine gelungene Einführung in ein interessantes Gebiet der modernen Stochastik und mathematischen Physik und stellt einen fest umrissenen Gegenstand umfassend dar, vor allem den analytisch-methodischen Aspekt. ... Die Beweise sind übersichtlich und gut gegliedert, was das Nachvollziehen der Argumente sehr erleichtert; die didaktische Leistung der Autoren in diesem Punkt ist beeindruckend. Ein sorgfältig zusammengestelltes Literaturverzeichnis von etwa 400 Titeln schließt das Buch ab. Ingesamt ein sehr gut geschriebener und nützlicher Band."
DMV Jahresbericht, 103. Band, Heft 3, November 2001