Stochastic Processes on a Lattice and Gibbs Measures

  • Bernard Prum
  • Jean Claude Fort

Part of the Mathematical Physics Studies book series (MPST, volume 11)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Bernard Prum, Jean Claude Fort
    Pages 1-18
  3. Bernard Prum, Jean Claude Fort
    Pages 19-39
  4. Bernard Prum, Jean Claude Fort
    Pages 40-57
  5. Bernard Prum, Jean Claude Fort
    Pages 58-81
  6. Bernard Prum, Jean Claude Fort
    Pages 82-98
  7. Bernard Prum, Jean Claude Fort
    Pages 99-119
  8. Bernard Prum, Jean Claude Fort
    Pages 120-135
  9. Bernard Prum, Jean Claude Fort
    Pages 136-160
  10. Bernard Prum, Jean Claude Fort
    Pages 161-173
  11. Bernard Prum, Jean Claude Fort
    Pages 174-204
  12. Back Matter
    Pages 205-220

About this book

Introduction

In many domains one encounters "systems" of interacting elements, elements that interact more forcefully the closer they may be. The historical example upon which the theory offered in this book is based is that of magnetization as it is described by the Ising model. At the vertices of a regular lattice of sites, atoms "choos e" an orientation under the influence of the orientations of the neighboring atoms. But other examples are known, in physics (the theories of gasses, fluids, .. J, in biology (cells are increasingly likely to become malignant when their neighboring cells are malignant), or in medecine (the spread of contagious deseases, geogenetics, .. .), even in the social sciences (spread of behavioral traits within a population). Beyond the spacial aspect that is related to the idea of "neighboring" sites, the models for all these phenomena exhibit three common features: - The unavoidable ignorance about the totality of the phenomenon that is being studied and the presence of a great number of often unsuspected factors that are always unquantified lead inevitably to stochastic models. The concept of accident is very often inherent to the very nature of the phenomena considered, so, to justify this procedure, one has recourse to the physicist's principle of indeterminacy, or, for example, to the factor of chance in the Mendelian genetics of phenotypes.

Keywords

Stochastic processes ergodicity statistics stochastic process thermodynamics

Authors and affiliations

  • Bernard Prum
    • 1
  • Jean Claude Fort
    • 1
  1. 1.Université Paris VParisFrance

Bibliographic information