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Scaling Limits of Interacting Particle Systems

  • Book
  • © 1999

Overview

Authors:
  1. Claude Kipnis

    1. Instituto de Matematica Pura e Aplicada, Rio de Janeiro, Brasil
      CNRS UPRES-A 6085, Université de Rouen, Mont Saint Aignan Cedex, France

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  2. Claudio Landim

    1. Instituto de Matematica Pura e Aplicada, Rio de Janeiro, Brasil
      CNRS UPRES-A 6085, Université de Rouen, Mont Saint Aignan Cedex, France

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  • This book is long-awaited in the "interacting particle systems" community.
  • Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator.
  • It presents the techniques used in the proff of the hydrodynamic behaviour of interacting particle systems.

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Introduction

    • Claude Kipnis, Claudio Landim
    Pages 1-6

  3. An Introductory Example: Independent Random Walks

    • Claude Kipnis, Claudio Landim
    Pages 7-20

  4. Some Interacting Particle Systems

    • Claude Kipnis, Claudio Landim
    Pages 21-40

  5. Weak Formulations of Local Equilibrium

    • Claude Kipnis, Claudio Landim
    Pages 41-46

  6. Hydrodynamic Equation of Symmetric Simple Exclusion Processes

    • Claude Kipnis, Claudio Landim
    Pages 47-66

  7. An Example of Reversible Gradient System: Symmetric Zero Range Processes

    • Claude Kipnis, Claudio Landim
    Pages 67-114

  8. The Relative Entropy Method

    • Claude Kipnis, Claudio Landim
    Pages 115-139

  9. Hydrodynamic Limit of Reversible Nongradient Systems

    • Claude Kipnis, Claudio Landim
    Pages 141-189

  10. Hydrodynamic Limit of Asymmetric Attractive Processes

    • Claude Kipnis, Claudio Landim
    Pages 191-229

  11. Conservation of Local Equilibrium for Attractive Systems

    • Claude Kipnis, Claudio Landim
    Pages 231-256

  12. Large Deviations from the Hydrodynamic Limit

    • Claude Kipnis, Claudio Landim
    Pages 257-285

  13. Equilibrium Fluctuations of Reversible Dynamics

    • Claude Kipnis, Claudio Landim
    Pages 287-310

  14. Back Matter

    Pages 311-445
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Keywords

About this book

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.

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

Authors and Affiliations

  • Instituto de Matematica Pura e Aplicada, Rio de Janeiro, Brasil

    Claude Kipnis, Claudio Landim

  • CNRS UPRES-A 6085, Université de Rouen, Mont Saint Aignan Cedex, France

    Claude Kipnis, Claudio Landim

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