Discrete Probability Models and Methods

Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding

  • Pierre Brémaud

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 78)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Pierre Brémaud
    Pages 1-19
  3. Pierre Brémaud
    Pages 21-63
  4. Pierre Brémaud
    Pages 65-77
  5. Pierre Brémaud
    Pages 79-92
  6. Pierre Brémaud
    Pages 93-115
  7. Pierre Brémaud
    Pages 117-144
  8. Pierre Brémaud
    Pages 145-183
  9. Pierre Brémaud
    Pages 185-214
  10. Pierre Brémaud
    Pages 215-253
  11. Pierre Brémaud
    Pages 255-286
  12. Pierre Brémaud
    Pages 287-317
  13. Pierre Brémaud
    Pages 319-339
  14. Pierre Brémaud
    Pages 341-355
  15. Pierre Brémaud
    Pages 357-371
  16. Pierre Brémaud
    Pages 373-396
  17. Pierre Brémaud
    Pages 397-415
  18. Pierre Brémaud
    Pages 417-440
  19. Pierre Brémaud
    Pages 441-455
  20. Pierre Brémaud
    Pages 457-474
  21. Pierre Brémaud
    Pages 475-508
  22. Pierre Brémaud
    Pages 509-534
  23. Back Matter
    Pages 535-559

About this book


The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory.

The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book. 


60J10, 68Q87, 68W20, 68W40, 05C80, 05C81, 60G60 60G42, 60C05, 60K05, 60J80, 60K15 probabilistic methods Markov chains random graphs random walks Boltzmann sampling probability on graphs coupling method discrete probabilty

Authors and affiliations

  • Pierre Brémaud
    • 1
  1. 1.INRIA, École Normale SupérieureParisFrance

Bibliographic information

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