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.Read more
- Systematically presents probabilistic and graph theory tools for percolation, and that describes Smirnov's results in conformal invariance
- Streamlined presentation requiring only minimal background in probability and graph theory
- Numerous examples illustrate the important concepts and enrich the arguments
Reviews & endorsements
'This book contains a complete account of most of the important results in the fascinating area of percolation. Elegant and straightforward proofs are given with minimal background in probability or graph theory. It is self-contained, accessible to a wide readership and widely illustrated with numerous examples. It will be of considerable interest for both beginners and advanced searchers alike.' Zentralblatt MATH
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: September 2006
- format: Hardback
- isbn: 9780521872324
- length: 334 pages
- dimensions: 235 x 161 x 20 mm
- weight: 0.66kg
- contains: 112 b/w illus.
- availability: Available
Table of Contents
1. Basic concepts
2. Probabilistic tools
3. Percolation on Z2 - the Harris-Kesten theorem
4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky
5. Uniqueness of the infinite open cluster and critical probabilities
6. Estimating critical probabilities
7. Conformal invariance - Smirnov's theorem
8. Continuum percolation
List of notation.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×