Percolation
eBook - PDF

Percolation

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Percolation

About this book

Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book, first published in 2006, are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.

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Yes, you can access Percolation by Bela Bollobás,Oliver Riordan in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Frontmatter
  3. Contents
  4. Preface
  5. Basic concepts and results
  6. Probabilistic tools
  7. Bond percolation on ℤ2 – the Harris–Kesten Theorem
  8. Exponential decay and critical probabilities – theorems of Menshikov and Aizenman & Barsky
  9. Uniqueness of the infinite open cluster and critical probabilities
  10. Estimating critical probabilities
  11. Conformal invariance – Smirnov's Theorem
  12. Continuum percolation
  13. Bibliography
  14. Index
  15. List of notation